Prestressed stayed compression members are frequently required as very slender load-bearing structural components by both investors and architects. Behavior of these members depends on their geometrical and material properties, prestressing and boundary conditions. In the paper are discussed respective critical buckling loads and post-buckling paths with regards to 2D and 3D GMNIA (geometrically and materially nonlinear analysis with imperfections) using ANSYS software. Former tests and recent detailed analyses of other authors are commented with respect to the 3D analysis, level of imperfections, boundary conditions at central crossarm (fixed or sliding stays) and nonlinear stainless steel material.