The flow of a non-Newtonian, power-law conducting fluid under the effect of a constant transverse magnetic field is considered. The flow is produced by a plate moving with constant velocity in a calm fluid. The plate is porous and fluid can either be sucked or injected through it. The boundary layer equations are transformed into a nondimensional form and are solved with a finite difference method. Part of this problem has been investigated in the past but only for suction and pseudo-plastic fluids. However, all flows of the present work reach an asymptotic state and exact analytical solutions exist for Newtonian fluids. In the present work we extend the investigation to both pseudo-plastic Newtonian and dilatant fluids in both suction and injection cases.