Laser heating for an infinite solidx>0 is modeled by imposing the heat source distributionE0(1−R)&agr; exp(−&agr;x) within the material. In order to overcome the problem of superheating in the solid, when the intensity is strong enough to cause a change of phase, a ‘‘mushy zone’’ of partially molten material is postulated between the fully liquid and the solid phases. The model is applied to laser heating of a solid, initially at constant temperature, together with ablation of any fully liquefied material. The equations are transformed so as to be amenable to numerical methods and the resulting solutions analyzed. The model seems particularly appropriate to optically thin materials.