Hot isostatic pressing of metallic or ceramic porous preforms occurs by the densification of a shell at the surface of the preform, which then thickens until the whole sample is fully densified. It is shown that the development of such a dense shell can reduce the pressure acting to densify the remaining porosity. Furthermore, this pressure difference can lead to anisotropic creep of the shell, and this may be a contributory cause of shape change of samples during HIPing. The stresses occurring during cooling of the sample and the residual stresses, are calculated as a function of various input parameters. It is found that the cooling stresses can be particularly large and tensile, and may be the cause of surface cracking observed in certain HIPed ceramic samples.