The approximate method of computing multiple span beams with variable cross section and elastic supports and connections, in any area of contact with the elastic foundation for static loads and temperature variation effects was elaborated by the author at the Leningrad Department of the Gidroproekt. For this purpose a foundation model based on Winkler's hypothesis, an elastic, isotropie medium of finite depth, one of infinite depth (the plane and the space probtems),~and a combined medium (the plane and the space problems) were investigated. The method is based on the general theory of structural mechanics of bar systems with the application of the integral equations of Fredholm and of the methods of numerical analysis. The computational formulas are given in matrix form. The above mentioned method is completely developed in the B-l-10 program for the BESM-2M computer. Let us examine a multiple span beam of variable height h(x) and constant width bb having a portion of its length supported by an elastic foundation and undergoing the influence of a complex of external factors F. The external factors include concentrated and distributed forces Pi, q(x) and moments Mi, m(x), temperature gradients AT(x), initial rotations vl(x) and displacements v~.(x) of the supports and connections, the load on the foundation surface qel(X). We will consider the connections and supports as elastic and completely independent of the foundation (Fig. la). As unknowns we select the normal forces r(x) which appear at the contact between the beam and the foundation and the internal forces xi (0-<i _<n) in the supports and connections. Tim friction on the contact surface is neglected. It we assume that r(x) is a known function, the structure can be considered as a multiple span beam (Fig. lb): We consider the basic system as a cantilever beam with a connection at the right. In the case when there is no connection we introduce fictitious constraints preventing the rotation or the vertical displacement. The rotation angle ~ and the vertical displacement v of the actual constraints will be supplementary unknowns. The reduced system of canonical equations of the mixed method with respect to Xi, ~, and v will be in the most general case 7: