Numerical solution of variational inequalities of obstacle type associated with some free boundary problems with nonlinear source terms is considered. Iterative methods based on the combination of the domain decomposition technique and the Newton-like approach are proposed for solving discrete obstacle problems arising from the continu-ous, piecewise linear finite element approximation of the problems. The calculation pro-cesses are easily to be parallelized. The convergence and specially the convergent rate of the algorithms are obtained.