Abstract In general the temperature profile within a steel beam subjected to fire is non-uniform. To predict the structural behaviour of such a beam the effect of the variation of the steel's characteristics with temperature across the beam must be considered. In addition stresses due to non-uniform thermal expansion need to be included. A procedure for the analysis of such cross-sections with a non-uniform temperature profile is presented. This has been developed specifically to be used on personal computers, rather than the mainframes normally employed for numerical analysis of this degree of complexity. The actual temperature profile is idealised by a finite number of constant temperature steps, and the thermal stresses induced are converted to a set of external loads. These are used in a secant stiffness approach to predict the deflection-temperature characteristics of beams. A comparison with test results for different types of beam illustrates the degree of accuracy that can be achieved using the techniques described.