Solid electrolytes in combination with alkali-metal anodes offer the potential to enhance battery energy density and safety. The inherent challenges associated with cell pressure management have to be accounted for in the cell design but are not sufficiently understood. Here we present a theoretical study linking the effects of thermal and chemo-mechanical expansion of electrode materials to the stresses acting on tubular and planar solid electrolytes, at the example of the sodium-nickel chloride battery chemistry. Based on our analysis, we derive three strategies to reduce these stresses. Namely, we propose (i) to increase the cell closing temperature during production (ii) to reduce the gas pressure in the cell (e.g. by applying a vacuum), and (iii) to rationally balance the volume of the two electrode compartments. Mechanical considerations developed herein form the foundation for the development of next-generation battery cell designs.