A two-dimensional numerical model has been developed to study mantle convection during continental collision and breakup. The model incorporates rigidly moving continental and oceanic plates with distinct thermal and mechanical properties, and finite thickness. We systematically investigate the influences of continental width, diffusivity, thickness and internal heating on continental collision and breakup. In addition, we consider the influence of different degrees of internal heating in the mantle. For each case considered we model a pair of identical continents being carried towards a site of plate convergence by underlying counter-rotating mantle convection cells. The continents collide at the mid-plane of the model to form a motionless, rigid, conducting supercontinent whereas oceanic plate material continues to recycle through the mantle. We find that changes in the mechanical boundary conditions at the upper surface are important factors in initiating flow reversals below the supercontinent. More generally, our findings, based on 144 models, are that the following factors favour the initiation of flow reversals below the supercontinent: wider continents, lower thermal diffusivity of continental plates, thicker plates and continental crustal heating. Furthermore, lower percentages of internal heating in the mantle are necessary to sustain and promote the subcontinental flow reversals in our models.