The unsteady viscous compressible boundary layer fluid flow past a semi-infinite vertical porous plate surrounded in a porous medium with induced magnetic field has been studied numerically. The governing non-linear coupled partial differential equations have been transformed by using usual transformations. The obtained non-linear dimensionless coupled partial differential equations have been solved numerically. The explicit finite difference method is used as solution technique and MATLAB software is used as a secondary tool. The obtained results for the density, velocity, induced magnetic field as well as temperature distributions are shown graphically.