A theory of the generation and propagation of two and three dimensional magnetohydrodynamic surface waves due to an arbitrary as well as special oscillatory pressure distribution acting on the free surface of an inviscid electrically conducting fluid is presented. The unsteady solutions for two as well as three dimensional free surface elevation are obtained explicitly. The asymptotic behaviour of these solutions for large time and distance are determined to describe the qualitative and quantitative nature of the wave motions. The solutions consist of both the steady-state and the transient components. The latter is found to decay asymptotically for large time, and the steady-state is reached. Magnetohydrodynamic surface waves in deep and shallow fluid are dispersive in nature.