The mathematical model of deformation, the research and analysis steadiness angorythm of ribbed shells taking into account both geometrical and physical nonlinearities based on the variational statement of the problem and it solving by Ritst method. As a result the task was reduced to the set of nonlinear algebraical equations. Some examples of proposed equations solutions are obtained; the comparative analysis was given for the reinforced concrete and metal shells. It is shown that peculiarities of nonlinear structure behavior have a great impact on the decrease of the critical load found by solving physical linear problem.