In this paper, the mathematical model of shakedown optimization problem of limit analysis for the thin-wall metal frames under variable quasi-static loads is presented. Authors assume the elastic-plastic flexural buckling in one plane without lateral torsional buckling behavior of members on conditions of the ideal elastic-plastic behaviour of the frames materials. According to Eurocodes requirements, the features of these frames taking into account rigidity of their foundations are described. There is problem with definition equivalent uniform moment factors for frames under variable quasi-static loads, because moment diagram is not constant. Classification of joints by stiffness was analyzed. The cases when the conditions of rigidity are not satisfied were described. The variants of solving tasks for thin-wall metal frames have been developed, for which there is a discrepancy between the classification by stiffness of the column base and the initial design model. It’s demonstrated on the principle scheme of the iteration process. With the help of numerical example, the problems which deal with classification of joints by stiffness on the final step of the optimal design of the thin-wall metal frames were performed.