The main aim of the present research is to develop a method of analysis for structural frames exposed to fire including the effects of material and geometric non-linearities. A matrix stiffness method based on a secant stiffness approach is used providing a full temperature deformation history. The approach has previously been used for the analysis of continuous beams and is extended in the present work to include axial forces. These not only affect the longitudinal displacement, but also reduce the member stiffness and create secondary moments due to the p-delta effect. The influence of material unloading on the moment-axial force-curvature relationship is studied by examining a cross-section subjected to different combinations of bending moment and axial force at both ambient temperature and in fire. A computer program, based on the method is used to conduct a limited parametric study. This includes the influence of slenderness ratio, the magnitude of axial load and moment, the size of cross-section and grade of steel. Both uniform and non-uniform temperature profiles are considered for isolated beams, columns and simple portal frame. The importance of the p-delta effect is also investigated.