As a steerable needle or robotic manipulator, the concentric-tube robot shows good potential for use in minimally invasive medical procedures. However, the torsional deformation of the precurved tubes comes at the price of instability, which not only limits the workspace and tool path but also potentially creates danger of tissue rupture when external load is applied. In this paper, we propose anisotropic patterning of tubes to solve the instability problem. Hole-patterning can tune the mechanical properties of the tubes so that the ratio of the torsional rigidity to the bending rigidity becomes higher. This study investigates the effect of pattern design parameters by building a lumped analytical model and examining it with finite-element analysis. The pattern is engraved via laser machining and we experimentally verify that material anisotropy reduces instability.