A galvanic element is provided having a solid-state cell stack containing a multiplicity of electrochemical solid-state cells stacked along a longitudinal axis in a housing. Each of the electrochemical solid-state cells has a stack including at least one anode layer, at least one cathode layer and at least one solid electrolyte layer arranged between the anode layer and the cathode layer. At least one of the electrochemical solid-state cells includes an elastically deformable compensation element, which at least partly compensates for a change in volume along the longitudinal axis of the stacked electrochemical solid-state cells. A method for producing such galvanic elements is also provided. Advantageous applications are found in vehicles and mobile devices including such galvanic elements.