Boundary layer analysis of a flow of viscous electrically conducting fluid past a continuously moving semi-infinite plate under the influence of (i) transverse magnetic field (ii) variable viscosity is presented here. Local non-similarity equations are solved numerically on a computer and the velocity, temperature profiles are shown on graphs and the numerical values of the skin-friction coefficient and the Nusslet number are listed in a Table. It is observed that velocity decreases, temperature increases, skin-friction coefficient increases and the Nusselt number decreases with increasing the variable viscosity parameter θ_r .