The present paper deals with the analysis of load carrying capacity of a steel column under compression with a thin-walled open and closed cross-sections, the axis of which is randomly three-dimensionally curved. The initial curvature was modelled by means of random fields, applying the Latin Hypercube Sampling method. The load carrying capacity of the compression column has been calculated by geometrically nonlinear solution, applying the ANSYS program. The element BEAM 188 from the ANSYS element library was used for the solution. The load carrying capacity statistical characteristics of columns with open and closed cross-sections have been compared. The results are presented in the table.