Sears Roebuck and Co. has been offering various forms of two-wheeled motor vehicles in their catalogs over the years. They first introduced the "1910 Model Sear Auto-Cycle" for $169 in their 1909 catalog, The Great Price Maker. Sears later discontinued selling motorcycles in Spring 1914. Sears wouldn't begin offering any other two-wheeled motor vehicles until 1951 when they introduced the Allstate Scooter manufactured by Cushman.
In the 1950s and 1960s, Sears sold many rebadged motorcycle, moped, and scooter models produced by manufacturers including Cushman, Piaggio, Gilera, Puch, Yardman and others. From 1951, their catalog bikes were rebadged with "Allstate" up until the mid 1960s, then switching to the "Sears" badge.
Each one of these two-wheeled motor vehicles sold by Sears Roebuck and Co. during the 1950s and 1960s were assigned an identifying model number. This model number was marked in the Sears catalog with the cycle for ordering purposes. Once you received your cycle, you could find the model number on a metal plate riveted to the cycle and printed on the corresponding setup/parts manual. Here are what the riveted badges look like:
These model numbers were very important because they were used throughout the whole process from ordering the two-wheeled vehicle from Sears up until you needed help from the Sears Cycle Center getting the correct replacement parts. These model numbers weren't used for titling purposes because there was still a separate serial number engraved on the two-wheeled vehicle that came from the manufacturer.