A pseudo-spectral method for a solution of the equations of dynamic elasticity in cylindrical coordinates is based on the Chebychev expansion in the radial direction and the Fourier expansion in the angular direction and is suitable for simulating wave propagation in the vicinity of cylindrical objects. The numerical grid consists of a series of concentric rings, each one with a separate Chebychev-Fourier mesh. One numerical grid is defined for the cylindrical cavity and another grid for the medium around the cavity. Combining these two numerical grids allows reduction of the number of grid points in the angular direction in the interior grid and thus increases the time step. This makes the use of polar coordinates much more economic.The numerical algorithm is applicable to any arbitrary heterogeneous medium.