In this paper, we deal firstly with the question of the stability of the metric regularity under set-valued perturbation. By adopting the measure of closeness between two multifunctions, we establish some stability results on the semi-local/local metric regularity. These results are applied to study the convergence of iterative schemes of Newton-type methods for solving generalized equations in which the set-valued part is approximated. Some examples illustrating the applicability of the proposed method are discussed.