Enveloping machine for enveloping plates for electric storage batteries, which comprises: - a support structure, intended to be abutted against the ground; - supply means for supplying a separator strip; - a storage susceptible of housing a plurality of plates for electric storage batteries; - a manipulation station for manipulating the plates, which comprises gripping means adapted to separately pick up the plates from said storage; - an enveloping station mounted on said support structure and susceptible of receiving the plates from said gripping means and of receiving the separator strip from said supply means in order to enclose the single plates with the separator strip; said enveloping machine being characterized in that said storage is susceptible of housing said plates placed substantially vertically in succession one next to the other; said gripping means comprising: - at least one movable trolley actuated to translate by means of first actuator means between said storage and said enveloping station along a first movement direction; - at least one rotary head, rotatably mounted on said movable trolley and actuated to rotate by means of second actuator means between a grip position, in which it is susceptible of picking up the single plates vertically placed in said storage, and a release position, in which it is susceptible of horizontally depositing the single plates at said enveloping station. - a support structure, intended to be abutted against the ground; - supply means for supplying a separator strip; - a storage susceptible of housing a plurality of plates for electric storage batteries; - a manipulation station for manipulating the plates, which comprises gripping means adapted to separately pick up the plates from said storage; - an enveloping station mounted on said support structure and susceptible of receiving the plates from said gripping means and of receiving the separator strip from said supply means in order to enclose the single plates with the separator strip; said enveloping machine being characterized in that said storage is susceptible of housing said plates placed substantially vertically in succession one next to the other; said gripping means comprising: - at least one movable trolley actuated to translate by means of first actuator means between said storage and said enveloping station along a first movement direction; - at least one rotary head, rotatably mounted on said movable trolley and actuated to rotate by means of second actuator means between a grip position, in which it is susceptible of picking up the single plates vertically placed in said storage, and a release position, in which it is susceptible of horizontally depositing the single plates at said enveloping station. - at least one movable trolley actuated to translate by means of first actuator means between said storage and said enveloping station along a first movement direction; - at least one rotary head, rotatably mounted on said movable trolley and actuated to rotate by means of second actuator means between a grip position, in which it is susceptible of picking up the single plates vertically placed in said storage, and a release position, in which it is susceptible of horizontally depositing the single plates at said enveloping station.