For laser intensities in the range of 10(8)-10(9) W/cm(2), and pulse lengths of order 10 mu sec or longer, we have modified the inertial confinement fusion code Lasnex to simulate gaseous and some dense material aspects of the laser-matter interaction. The unique aspect of our treatment consists of an ablation model which defines a dense material-vapor interface and then calculates the mass flow across this interface. The model treats the dense material as a rigid two-dimensional mass and heat reservoir suppressing all hydrodynamic motion in the dense material. The computer simulations and additional post-processors provide predictions for measurements including impulse given to the target, pressures at the target interface, electron temperatures and densities in the vapor-plasma plume region, and emission of radiation from the target. We will present an analysis of some relatively well diagnosed experiments which have been useful in developing our modeling. The simulations match experimentally obtained target impulses, pressures at the target surface inside the laser spot, and radiation emission from the target to within about 20%. Hence our simulational technique appears to form a useful basis for further investigation of laser-surface interaction in this intensity, pulse-width range.