Method of perturbations in boundary value problems of impact deformation of incompressible elastic mediums

On an example of a solution of the one-dimensional task with a rotational symmetry about antiflat impact loading of an incompressible elastic medium till it cylindrical boundary surface the singularities are considered informations of the similar tasks to the singular tasks of a method of perturbations. The recurrent solutions of nonlinear developmental the equations, implying at sequential application of developed variant of a method of perturbations, appear as interior expansion near to wave front.