Abstract :The effect of magnetic field on torsional waves propagating in non-homogeneous viscoelastic cylindrically aeolotropic material is discussed. The density and elastic constant of the viscoelastic specimen are non-homogeneous. Bessel functions are taken to solve the problem and frequency equations have been derived in the form of a determinant. Dispersion equation in each case has been derived and the graphs have been plotted showing the effect of variation of elastic constants and the presence of magnetic field. The obtained dispersion equations are in agreement with the classical result. The numerical calculations have been presented graphically by using MATLAB.