Abstract: The object of the invention is a process for production of a bottle stopper, particularly for wine bottles, from polymers, characterized in that it comprises the following series of steps: a) homogenizing and/or mixing a single polymer material based on at least VAE (vinyl acetate ester), by bringing it to temperature, in an extruder comprising a single casing and one screw as well as an outlet nozzle, b) injecting at least one gas under pressure into this single material, c) shaping the material through the nozzle of said extruder in the form of an extrusion of predetermined diameter, and d) cutting of said extrusion to form stoppers of this same diameter. The invention also covers the associated device.