The stress-induced change in chemical shielding induced by sample spinning is measured and interpreted theoretically. By considering the rotating sample as an elastic body in the plane-strain approximation, the internal stress field as a function of sample size, rotation frequency, and elastic constants is determined. This stress field and the dependence of chemical shielding on strain, as determined by first-principles calculations, are combined to predict the shielding dependence on rotation frequency under isothermal conditions in single crystal gallium phosphide. The prediction is in good qualitative agreement with the experiment. Little to no effect is detected in powder samples of both gallium phosphide and copper iodide, and it is argued that this follows from the stress distribution in granular material, as opposed to bulk crystals. Finally, the temperature and pressure dependence of the chemical shielding is estimated from these considerations and found consistently to underestimate the experimental values, indicating the importance of finite-temperature anharmonic effects even in very simple solids.