The Sears 340 was made by Ithaca as the Model 49ss (for stainless steel). It was made from 1961-78, and is a Martini action single shot lever rifle. For more info, research under the Ithaca designation.
In my opiniont the above statement about ss meaning stainless steel is wrong. SS in this case probably means "single-shot." The Model 49 by Ithaca was a single-shot .22 rifle, a lever-action but with a Martini action. It was never made in stainless steel. It was made from 1961-78. As for the Sears Model 340 I do not know about that gun but one could look in the Standard Catalog of Firearms and find out or find one of many web sites that give crossover information on Department Store/Catalog House guns that had their brand name on but were made by some large gun company. One of Sears' brand names, for example, was J. C. Higgins.
I concur with the 2nd poster. SS means Single Shot. The Sears model 340.xxxxx is a clone of the Model 49 and made by Ithaca with the Ted Williams signature on the barrel. The only difference is the absence of the fake ammo tube and the Sears model has a heavy "bull" barrel. Despite what is stated about "house brands" not being collectible since I got interested in Ithaca's in 1993 I have only seen 3 of these rifles.
If it is in VG shape to ask $175 would not be unreasonable.
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