Whether or not the classical theory of elasticity is valid for static granular matter is a basic question of granular physics. We present in this work stress distributions inside hollow cylindrical (Couette geometry) specimens， calculated with the nonlinear elastic equations recently reported in literature. Most of these results can be experimentally measured， and are useful for clarifying the basic question by testing the applicability of the nonlinear elastic equations to granular matter. Moreover they can also be used for analyzing the lateral pressure coefficient of interest in soil engineering.