Nonsmooth equations with finitely many maximum functions is often used in the study of complementarity problems, variational inequalities and many problems in engineering and mechanics. In this paper, we consider the global convergence methods for nonsmooth equations with finitely many maximum functions. The steepest decent method and the smoothing gradient method are used to solve the nonsmooth equations with finitely many maximum functions. In addition, the convergence analysis and the applications are also given. The numerical results for the smoothing gradient method indicate that the method works quite well in practice.