Deformation of porous crustal rock through diagenesis, tectonic loading, or other processes can change pore volume and affect fluid pressure. The largest stress-induced pore pressure changes occur when fluid is trapped in pores in an "undrained" condition. We have measured the undrained poroelastic response of two sandstones to changes in mean and deviatoric stress. Pore pressure was found to respond to mean stress ??m in the usual manner: ??p = B ?? ??m (B ranging from 0.4 to 0.7), nearly independent of the ambient deviatoric stress state. However, variations in deviatoric stress (??d = (??1 - ??3)/2) at constant mean stress were also found to induce a reversible (elastic) pore pressure response to stress levels up to and exceeding 80% failure stress (i.e., ??p = ??????d/??m = const.). The coefficient ?? became more negative with increasing deviatoric stress level in sandstone and Ottawa sand samples. That is, ?? represents a dilatant response where increased deviatoric stress causes a decrease in pore pressure. The poroelastic response to deviatoric stress is explained in terms of anisotropic matrix stiffening due to closure of crack-like pore space or flattening of grain contacts at high ambient stress levels and can be important in calculations of earthquake stress transfer.