Over the last several years a 2-D finite difference acoustic propagation program for finite amplitude interactions has been developed at the University of Illinois and USA-CERL. In this presentation the addition of the numerical coupling of the air to the hard surface and porous media models of the ground will be described. The porous model used was the time-dependent form of the phenomenological model presented by Morse and Ingard as interpreted by Attenborough for low frequencies [K. Attenborough, J. Acoust. Soc. Am. 73, 785–799 (1983)]. Simulation results will be presented for the nonlinear pressure variations evident due to the cumulative interactions along the air-ground interface for small explosions, when the ground was either hard or porous. [Computations performed at the National Center for Supercomputing Applications, Champaign, IL.]