Abstract: Prerented in this paper is a simplified practical method, in which the stress-strain relation of roil obeye the theory of elastic halfspace and an equivalent continuum is u ed for the mathematical models of frame, The rigidity matrix of sail is ddrived by analytical method. The interaction of multi tory frame and box-foundation is solved by the least Square colllcation method.In this paper, the following three mathematical models are investigated:1.The rigidity of frame is ignered2.Only shear rigidity of frame is taken into account.3.Both the shear rigidity of frame and the axial stiffness of columns are taken into account.Finally several examples are given for comparison.