Enveloping machine for enveloping plates for electric storage batteries, comprising a storage for storing plates for electric storage batteries, and a manipulation station for manipulating the plates, which comprises a gripping device for separately picking up the plates from the storage and for depositing them at an enveloping station, which also receives a separator strip in order to enclose the plates with the separator strip itself. In addition, the gripping device comprises a movable trolley actuated to translate between the storage and the enveloping station, and a rotary head mounted on the movable trolley and actuated to rotate between a grip position, in which it picks up the plates placed vertically in the storage, and a release position, in which it deposits the plates horizontally on the enveloping station.