We present a nonlinear effective medium method to investigate properties of nonlinear surface magnetostatic waves of magnetic superlattice films, or magnetic multilayers. In the third-order approximation, the nonlinear expressions of alternating effective magnetization in the systems are obtained. On this basis, the nonlinear coefficients, wave number, and frequency shifts of surface magnetostatic waves are calculated numerically. A very interesting result is that magnetostatic surface envelope solitons are possible to exist in a certain frequency range since the Lighthill criterion is satisfied in this range. In the meanwhile, we find that there is a basic mistake in the previous theory related to the nonlinear surface magnetostatic waves of a single magnetic film.