Internal bores are widely seen across environmental science, oceanography and meteorology, and they are important in the prediction of severe weather, the global energy cascade in marine environments as well as the wear on manmade underwater structures. We aim to accurately model the propagation of an internal bore into a stratified fluid by building upon research which, to date, has been primarily focused on two-layer bore propagation. In a stratified bore, waves can form in the fluid above the bore and if the Froude number (analogous to the Mach number) is sub-critical these waves can influence the bore’s propagation. We successfully simulated both critical and sub-critical bores using a number of sets of fluid densities and initial bore heights. The results of these simulations will better our predictions of how these bores propagate and will help extend our knowledge on complex geophysical flows.