We propose an approach to solution of the problem of static stability of continuous plates and shells supported by regular lattice of beams (ribs), when the structures are subjected to thermal and force loading. We assume that the temperature field on the structure surface and the externally applied forces are given to an accuracy of the constant multipliers (based on these parameters, a complex parameter can be determined). It is proven that the number of parameters for both types of loading (force and temperature) can be increased. Examination of stability under multiparameter loading is made on the base of the known Papkovich theorem. The critical values of load under one-parameter loading are determined using the energy criterion in Bryan form. The components of stress-strain state of structure are determined by using finite element method. In order to take into account the peculiarities of the structures under examination, it is proposed to apply the composite finite elements, which make the fragments of continuous plates (shells) and lattice plates (shells) stiffly attached to each other. The relationships derived for calculation of the finite-element stiffness matrices do not presume application of the technique of `continualization’ (`smearing’) of a discrete set of ribs. This fact allows us to estimate peculiarities of the work of each region of ribbing more exactly. Application of finite element procedure makes the approach proposed efficient when analyzing the structures of sufficiently complicated form under various force and geometrical boundary conditions.