We present results for an advection-reaction-diffusion model describing malignant tumour (i.e. skin cancer) invasion. Numerical solutions indicate that both smooth and shock-fronted travelling wave solutions exist for this model. We verify the existence of both type of these solutions using techniques from geometric singular perturbation theory and canard theory. Moreover, we provide numerical results on the stability of the waves and the actual observed wave speeds. This is joint work with K. Harley, G. Pettet, R. Marangell and M. Wechselberger.