A numerical model is presented to simulate the mechanical behaviour of composite steel and concrete columns taking into account the interaction between the hollow steel section and the concrete core. The model, based on displacement finite element methods with an Updated Lagrangian formulation, allows for geometrical and material non linearities combined with heating over all or a part of the section and column length. Comparisons of numerical calculations made using the model with 33 fire resistance tests show that the model is able to predict the fire resistance, expressed in minutes of fire exposure, of composite columns with a good accuracy.