The article presents the results of an analysis concerning changes in strength and stability of flat tubular rigid frame structural systems of sheds caused by changes in their geometric forms. In the considered cases, the examined shape changes consist in changing the inclination of the frame’s columns to the vertical, with their bases shifted inside and outside the systems. This is how a few derivative frame systems of special trapezial forms are created in relation to the basic rectangular frame characterized by vertical single-branch columns and a horizontal lattice girder. The specificity of the loads imposed on the flat systems is fastening of each roof cladding with each corrugation to the upper chord of the considered frame girder. Thus, the imposed load should be considered as a uniform distribution over the entire length of the chord. The presented results are to be used in the next steps of the research, where the flat transverse frame systems changing their shapes along the length of a building are to be analysed. The obtained results are going to be implemented in a future method for parametric shaping of unconventional forms of buildings and their optimized structural systems. The elaborated structures constitute a certain uniform area of analysis of flat lattice girders, selected from a large number of areas analysed or planned for research, including related to oblique lattice girders or frames with diversified static schemes.