When classical multigrid methods are applied to discretizations of variational inequalities, several complications are frequently encountered mainly due to the lack of simple feasible restriction operators. These difficulties vanish in the application of the cascadic version of the multigrid method which in this sense yields greater advantages than in the linear case. Furthermore, a cg-method is proposed as smoother and as solver on coarse meshes. The efficiency of the new algorithm is elucidated by test calculations for an obstacle problem and for a Signorini problem.