This paper presents a globally convergent successive approximation method for solving F(x) = 0 where F is a continuous function. At each step of the method, F is approximated by a smooth function f(k), with parallel to f(k) - F parallel to --> 0 as k --> infinity. The direction -f’(k)(x(k))F--1(x(k)) is then used in a line search on a sum of squares objective. The approximate function fi; can be constructed for nonsmooth equations arising from variational inequalities, maximal monotone operator problems, nonlinear complementarity problems, and nonsmooth partial differential equations. Numerical examples are given to illustrate the method.