In the present paper the flattening problem of steel tubes under lateral compression is taken as a part of the comprehensive studies on the crushing strength of structural elements, in which the finite element analysis and the crush tests are conducted for several circular and square tube specimens. All of the major factors in the quasi-static crushing problem such as large displacements, large strains and frictional contact are taken into account in the present finite element analysis. The obtained numerical solutions, which agree well with the experimental results with respect to the crushing deformations as well as the load-displacement relations, verify the validity of the nonlinear finite element method in the crush analysis. There remains some problems such as the effect of finite length for circular tubes, the influence of initial geometric imperfections and the thick-walled effect for square tubes, however, these problems are not so essential from a practical point of view. Therefore it can be concluded that the finite element code developed in the present study is useful for, the flattening analysis of a single tube at least with various cross-sectional shapes. The analysis of interactive behavior of several tubes and the dynamic analysis are the future problems.