An elliptic set of second-order equations in a cylinder of small height h is considered. Dirichlet conditions are specified on the lateral surface of the cylinder, and natural boundary conditions are specified at the ends. An algorithm for constructing a limiting problem in a section of the cylinder whose solution is an asymptotic approximation (as h → 0) to the solution of the initial problem is presented. In the case when the problem in the section is elliptic without a parameter, estimates of the rate of convergence are obtained. A program is compiled which, making the necessary calculations, constructs equations of the limiting problem.