Under certain conditions, laser light incident on a target material can induce an explosive removal of some material, a process called laser ablation. The photomechanical model of laser ablation asserts that this process is initiated when the laser-induced stresses exceed the strength of the material in question. Although one-dimensional calculations have shown that short pulsed lasers can create significant transient tensile stresses in target materials, the stresses last for only a few nanoseconds and the spatial location of the peak stresses is not consistent with experimental observations of material failure in biological tissues. Using the theory of elasticity, analytical expressions have been derived for the thermoelastic stresses and deformations in an axially symmetric three-dimensional solid body caused by the absorption of laser light. The full three-dimensional solution includes three stresses, radial, circumferential and shear, which are necessarily absent in the simple one-dimensional solution. These stresses have long-lived components that exist for eight orders of magnitude longer in time than the acoustic transients, an important point when the details of dynamic fracture are considered. Many important qualitative features are revealed including the spatial location of the peak stresses, which is more consistent with experimental observations of failure.