The serial number that I tried to get a good pic of on the back of the receiver under the stock is 'S 0346' - On the trigger guard on the left side of it on the receiver is a 'G' stamped into it. On top of the barrel is.Crack-Shot. J. Stevens Arms & Tool Co.22 Long Rifle. Chicopee Falls, Mass.

With the action open you should be able to see a letter code stamped on the inside of the receiver. Serial numbers came after 1968. I forget exactly,but the letter s=1968,give or take a couple letters,and each proceeding letter indicates a proceeding year. I lost the link to the page that gives the exact dates,but that is a rough estimation.
Stevens Serial Number Lookup Checking the serial number with the police department or sheriff’s office is beneficial if you’re considering buying a gun from a dealer because they can quickly check whether a gun was used for a crime or reported stolen in.

FIREARMS INFORMATION

Savage/Stevens single and double barrel shotguns were date coded between March 1949 and December 1968. Usually, it is behind the hinge pin or ahead of the trigger guard on the bottom of the frame. It will appear as a small circle containing a number and a letter. The letters correspond to the years shown in the following table as shown below. Significance of the numbers is not known.'*
*From page 1101 of Ned Schwing's 2004 Standard Catalog of Firearms, 14th Edition, published by Krause Publications of Iola, WI.

The letters indicate the year of manufacture starting with 'A' in 1949 and ending with 'X' in 1970. The letters 'O' and 'Q' were not used.

A 1949	I 1957	S 1965
B 1950	J 1958	T 1966
C 1951	K 1959	U 1967
D 1952	L 1960	V 1968
E 1953	M1961	W 1969
F 1954	N 1962	X 1970
G 1955	P 1963
H 1956	R 1964

More Random Internet Information ; I would like to add that I have found this circle, or oval, containing one or two numbers plus a single letter, just about anywhere and everywhere on the frame, but only on the outside of the frame, never inside. I have also found the circle or oval with letters and numbers on the barrel clusters, on the shot barrel or on the barrel assembly lug block. While the letter within the circle always match on factory matching barrel and frame, the numbers never match, or at least that has always been my experience. These Date Codes are also present on the Model 94 single shot frames and barrels, and I am sure on many others.
The marks on the inside of the frame, where the lower barrel seats when closed, are what I would call assembly stampings, and match frame to barrel, found on underside of shot barrel near forend lug, and also sometimes found on the butt stock under the butt plate. ~EE
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1. Stevens used plain numbers from their first double in 1878 until 1913.
2. Letter prefixes crept in on the serial numbers used on both hammer and hammerless doubles from 1913 to 1939. They always signified a change in mechanical design or manufacturing process which resulted in an interesting variants.
3. From 1940 to 1948 no serial numbers were used on doubles, only capital letters, usually in groups of three or four, the letter(s) sometimes enclosed in a circle, along with an inspector's symbol ( a heart , a diamond, a spade or some such ‘shape', on the bottom of the frame behind the hinge pin.
4. From 1948 to 1968 the letter symbols under the frame were changed to a ‘Capital letter with a one or two digit number' in a 1/4? circle. This was a date code which you will find illustrated in the Savage-Stevens-Fox pages of your Standard Catalog of Firearms.
5. From October 1968 to March 1988 Savage/Stevens/Fox B doubles are serial numbered in a completely new serial number range beginning at A000001. The six digit (always) numbers, stamped only on the left side of the frame, not on the barrels or fore end or on the wood, are preceded by capital letters from A to E. The letters do not correlate to production years. The letter prefix accompanied the Savage/Stevens/FoxB/Springfield serial number on every gun they made from 1968 on.

Beginning about 1978 numbers 1 to 20 were also stamped on the three major components, frame, barrels and fore end iron, to enable the factory to keep 20 guns of like model together in a group for packing in the standard 20 gun shipping carton.
Since I am interested only in double guns I stopped looking for numbers on Savage'Stevens doubles after 1988 because that's the year they shipped their last ‘Stevens Model 311'.
The highest number I have seen was on 20 gauge Stevens Model 311 Series H serial number E957971. The Savage branded imported doubles, over and unders or side by sides, are numbered differently. Each model is numbered in the range created by its manufacturer. As you probably have heard, Savage/Stevens' production records on their older models were destroyed in a sprinkler accident about 35 years ago, according to officers of the company.
To calculate an approximate number of ‘Stevens Model 311s' that were made from 1968 to 1988 you could do this math exercise. Since Savage used 5 letters (A to E), each on 999,999 guns, they must have made about 5 million guns. Perhaps 40% were doubles in the various Savage Brands and Private Brands. That makes 2 million doubles of which I estimate 80% were Stevens 311's. And that's not counting production before 1968. No wonder the “311” in its various variations is the all time favorite American made double.
And think how many Stevens 311s ( and Stevens made doubles that looked like Stevens 311s but carried private brands) had already been produced in the years between 1940 (first year of the ‘true' Stevens Model 311) and 1968, during which time they weren't serial numbered at all! There must be at least 4 million Stevens Model 311s, in one form or another, out there!
Stevens dropped the Springfield name on shotguns in 1948. Date codes didn't start until 1949.

The 'Date Codes' for the Stevens/Savage Model 24's are different, being the same as those found on the Lever Boss Codes for the Model 99 Savage lever-action rifles.

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Originated 05-17-04 Last updated 12-14-2020 ***
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Stevens Arms
Industry	Firearms manufacturer
Predecessor	J. Stevens & Co. (1864–1886) J. Stevens Arms & Tool Company (1886–1916) J. Stevens Arms Company (1915–1945) Stevens Arms (1945–1991; 1999–present)
Founded	1864; 157 years ago
Founder	Joshua Stevens
Headquarters	, U.S.
W.B. Fay and James Taylor
Products	Rifles, pistols, shotguns
Parent	Savage Arms
Website	http://www.savagearms.com

Stevens Arms was an Americanfirearms manufacturer founded by Joshua Stevens in 1864 in Chicopee, Massachusetts. The company introduced the .22 Long Rifle round and made a number of rifle, shotgun, and ta

Stevens Serial Number Lookup