This paper deals with buckling aspects of the design of stepped columns in heavy mill buildings. In these structures, columns have to carry significant axial loads that usually act eccentrically and strength reducing bending moments due to lateral loads. A simple physical model for buckling behaviour analysis is proposed and formulated using the differential equations of equilibrium. The exact solution of the governing equations is found by using symbolic computation. Effective buckling length coefficients and the corresponding critical loads are obtained and the results are presented in the form of design charts. The structural response is then evaluated and discussed for a number of practical cases for sway and sway prevented columns.