An energy method of analysis is presented which can be used to study the inelastic lateral-distortional buckling of hot-rolled I-sections continuously restrained at the level of the tension flange. The numerical modelling leads to the incremental and iterative solution of a fourth-order eigenproblem, with vey rapid solutions being obtainable, so as to enable a study of the factors that influence the strength of continuously restained I-beams to be made. Although hot-rolled I-scetions generally have stocky webs and are not susceptible to reductions in their overall buckling loads as a result of cross-sectional distortion, the effect of elastic restraints, particulartly against twist rotation, can lead to buckling modes in which the effect of distortion is quite severe. While the phenomenon has been studied previously for elastic lateral-distortional buckling, it is extended in this paper to include the constitutive relationship characteristics of mild steel, and incorporates both the so-called \'polynomial\' and \'simplified\' models of residual stresses. The method is validated against inelastic lateral-torsional buckling solutions reported in previous studies, and is applied to illustrate some inelastic buckling problems. It is noted that over a certain range of memeber slenderness the provisions of the Australian AS4100 steel standard are unconservative.