Packets of large amplitude internal waves have been observed in many coastal regions around the world. These wave packets typically generated by the interaction of stratified tidal flow with strong topographic features are highly nonlinear and their wave amplitudes often exceed 100 m. Previous attempts at modeling the large amplitude internal waves with the weakly nonlinear Korteweg-de Vries (KdV) equation have led to poor quantitative agreement. In this talk, I will introduce strongly nonlinear asymptotic models and describe their solitary wave characteristics in comparison with the fully nonlinear Euler equations and laboratory experiments. Then, I will present a local stability analysis of strongly nonlinear internal solitary waves and introduce a numerical scheme to suppress a Kelvin-Helmholtz- type instability. Some preliminary efforts will be also described to explain changes in surface roughness due to the interaction of surface waves with the surface currents induced by the internal wave motions.