The large-scale radiation-hydrodynamics computer code LASNEX, has been used to model experimental results in the laser ablation and fragmentation of renal and biliary calculi. Recent experiments have demonstrated laser ablation and fragmentation of human calculi in vitro and in vivo. In the interaction, laser light incident upon the calculus is of sufficient intensity to produce a plasma (a hot ionized gas). The physical picture which emerges is as follows. The plasma couples to acoustic and shear waves which then propagate through the dense stone material, causing spall and fracture by reflection from material discontinuities or boundaries. Experiments have thus far yielded data on the interaction against which models can be tested. Data on the following have been published: (1) light emission, (2) absorption and emission spectra, (3) fragmentation efficiency, (4) cavitation bubble dynamics and (5) mass removal. We have performed one dimensional simulations of the laser-matter interaction to elucidate the im-portant physical mechanisms. We find that good quantitative fits between simulation and experiment are obtained for visible light emission, electron temperature, electron density, plasma pressure and cavitation bubble growth. With regard to mass removal, experiment and simulation are consistent with each other and give an excellent estimate of the ablation threshold. The modeling indicates that a very small ablation layer at the surface of the calulus is responsible for significant mass loss by fragmentation within the bulk of the calculus. With such quantitative fits in hand, we believe this type of modeling can now be applied to the study of other procedures involving plasma formation of interest to the medical community.