The problems of non-stationary diffraction of acoustic waves in the inhomogeneous transversely isotropic spherical inclusion. The use of analytical solutions for the acoustic environment in a spherical coordinate system allows us to reduce the original problem to the integration of initial-boundary value problem for first order hyperbolic system with a special type of boundary conditions, containing the integral operators of convolution type in the time coordinate. To address the resulting initial boundary value problem the scheme such as the Courant-Isaacson-Rees. The solution of the problem for a sphere stiffness parameters which vary according to a power law.