The loss of stability of a cylindrical panel under the action of uniform pressure is considered. As a model, the nonlinear
theory of shells from elastomers of K.F. Chernykh is used. The cylindrical bending of the panel is investigated. The problem
reduces to solving a nonlinear one-dimensional boundary value problem for a system of nonlinear ordinary differential equations
and the associated nonlinear system of algebraic equations. The solution of the nonlinear boundary value problem is based on
method the solution continuation on the parameter and Newton-Kantorovich’s linearization. The corresponding linear boundary
value problems are solved using the Godunov’s orthogonal sweep method. The numerical solution of the problem is realized in
the MatLab environment. The results are presented in the form of ”load-displacement” diagrams characterizing the process of both
symmetric loss of stability and asymmetric bifurcation from a symmetric state. Deformed shell shapes are given at various points
in the loading diagrams