This paper reports the results of parametric analyses for the lateral torsional buckling strengths of singly symmetric stepped I-beams with constant depth subjected to general loading conditions. Simply supported beams with varying monosymmetric ratios from 0.1 to 0.9 were analyzed using a finite element program ABAQUS and a regression program MINITAB. Stepped length ratios, flange width ratios and flange thickness ratios were taken from the geometry of real bridges. The beams were first subjected to pure bending to take account for the effect of steps in beams. And then ten-different loading conditions were applied to the beams to study the effect of varied moment along the unbraced span. Design solutions were suggested based on the results of the parametric analyses. The use of equations for beams with inflection point of zero and one is recommended for stepped beams with monosymmetric ratios between 0.1 and 0.9. In specialty, the use of new equation for beams with inflection point of two is recommended for doubly stepped beams with monosymmetric ratios between 0.1 and 0.9 and for singly stepped beams with monosymmetric ratios between 0.1 and 0.7.