Linear stationary discrete-time descriptor systems with input sequences of random Gaus¬sian nonzero-mean vectors with bounded mean anisotropy are under consideration. Conditions of anisotropic norm boundedness for such systems are given in terms of generalized discrete-time alge¬braic Riccati equations (GDARE) and linear matrix inequalities (LMI). On basis of these results, the algorithm of anisotropic norm computation using convex optimization techniques is developed. Numerical examples illustrate methods of anisotropic norm computation.