The two-dimensional boundary layer flow past a wedge with slip velocity of a visco-elastic electrically conducting fluid in presence of a strong transverse magnetic field has been studied analytically. Similarly solutions are obtained by considering a special form of the magnetic field and slip velocity. Expressions for velocity and approximate skin friction coefficient at the wall of the wedge have been obtained and numerically worked out for different values of the flow parameters involved in the solution. The effects of the visco-elastic parameter on the velocity field have been presented graphically for various values of the flow parameters across the boundary layer.