The paper presents a semi-implicit algorithm for the nonlinear, three- dimensional dissipative magnetohydrodynamic equations in cylindrical geometry. The aim is to simulate the behaviour of a nonlinear MHD system which evolves on a time scale much larger than that associated with the fastest normal modes of the system e.g., growth and saturation of resistive instabilities, low frequency current drive models for fusion plasmas etc. The specific model is concerned with the low frequency, long wave length motion of an electrically conducting fluid permeated by a strong magnetic field so that the evolution of such a system is described by force-free MHD equations ignoring the pressure gradient term but incorporation compressibility. Thus the model can describe both shear and compressional Alfvén waves as well as resistive instabilities. The spatial approximation employs finite differences in the radial coordinate and spectral algorithm in the periodic polar and axial coordinates. To exhibit wave-like solutions, a leapfrog time discretization is used while the nonlinear advective terms are treated with a simple predictor-corrector method. A semi-implicit term is introduced as a simple modification to the momentum equation so that the resulting algorithm is unconditionally stable with respect to normal modes. The semi-implicit term retains much of the anisotropic character of the original MHD equations. The result of this study shows that for growth and saturation of resistive instabilities, the anisotropic operator in the semi-implicit scheme can tolerate about twice the time step as the isotropic operator for same accuracy. It is concluded that the method is simple, fast and accurate. The reviewer, however, fails to see in what way compressibility has been incorporated in the MHD equations since density is assumed uniform in space and time.