From the point of view of the method of continuation of the decision on the parameter, the systematization of existing solutions using step processes on the parameter . was carried out. Modifications of the method are constructed that implement a uniform process of continuation at regular and limit points of a set of solutions, and their generalization to nonlinear boundary problems. On the basis of these methods, algorithms for solving problems of large deflections, elastic arches and large axisymmetric deflections of rotation shells are given, which are used to study large deflections of circular arches and panels of tortoise shells. The use of the continuation of the solution on a geometric parameter is illustrated by the example of the problems of intrinsic oscillations and stability of parallelogram and trapezoidal membranes and panels.