The objective of this paper was to evaluate the potential for fully physical fire models to simulate the interactions between two converging fire fronts (a head fire and a back fire), in conditions similar to those encountered during suppression fire operations. The simulations were carried out using two fully physical models: FIRESTAR, in two dimensions, and Wildland Fire Dynamics Simulator, in three dimensions. Each modelling approach numerically solves a set of balance equations (mass, momentum, energy, etc.) governing the behaviour of the coupled system formed by the vegetation and the surrounding atmosphere. Two fuel profiles were tested: homogeneous grassland similar to landscapes in Australia and a shrubland representative of Mediterranean landscape (garrigue). Results from the two-dimensional and three-dimensional simulations were used to investigate how the two fire fronts interact together and mutually modify, or not, their own behaviour before merging. The results of these simulations showed that the merging of two fire fronts can result in a quick increase in fire-line intensity or in flame height. We concluded that physics-based simulations do reproduce reasonable and expected head- and back-fire interactions, but more work is needed to further understand the accuracy of such predictions.