The propagation of large amplitude internal solitary waves in a system of two constant density layers are studied using a strongly nonlinear long wave model.While steady solitary wave solutions of the model show excellent agreement with numerical solutions of the Euler equations and laboratory experiments, a local stability analysis reveals that the time-dependent inviscid model suffers from the Kelvin-Helmholtz instability due to a tangential velocity discontinuity across the interface.To suppress this undesirable short wave instability that is often absent in real experiments, an attempt is made to regularize the model by modifying the short wave behavior of the dispersion relation and introducing the effect of viscosity.