By use of the separation of variables method and the Laplace transformation, the two-dimensional transient torsional wave propagation problem in a transversely isotropic tube is studied when a torque is suddenly applied to its end surface. The results show that, for the discontinuous distribution of the impact shear stress, the region of the 2D stress distribution in a transversely isotropic tube becomes large with the increase of the anisotropy of the material.