For 1929, the J. Stevens Arms Co. introduced a cheaper version of their Springfield Arms Co. (earlier Riverside Arms Co.) No. 315, and called it the Springfield No. 311 --

This gun and its fancier versions the Springfield No. 315 and the Stevens No. 330 used the G.S. Lewis Patent No. 1,136,247 style action using coil spring driven strikers rather than internal hammers rotating about an axle. J. Stevens Arms Co. made many thousands of these G.S. Lewis action guns under their own names and many, many "trade brands." In 1936, J. Stevens Arms Co. brought out a new action with internal hammers that rotate about an axle, and replaced the Stevens No. 330 with the Stevens No. 530 and the Springfield No. 315 with the Springfield No. 515, while the Springfield No. 311 continued on to WW-II with the G.S. Lewis action. For 1940, the J. Stevens Arms Co. brought out a version of the Stevens No. 530 with the stock and forearm made of a synthetic wood look material they called Tenite --

After WW-II, Savage Arms Corp. decided to consolidate their gun making operations at their Stevens factories in Chicopee Falls, Mass., and the factory at Utica went to making washing machines and other household items for the post war housing boom. For 1947 the Savage/Stevens/Springfield/Fox catalogue offered the same Tenite stocked gun that had been the Stevens No. 530 M up to 1946 as a Springfield No. 311 --

By the 1948 Savage/Stevens/Fox catalogue the Tenite stocked double became the Stevens Model 311 --

By 1951 the Tenite stock was replaced with wood and the Model 311 became the gun most folks know.
So, there is the history of 311 as I know it.