This mathematical account of the mechanics of porous bodies looks at how porous bodies undergo irreversible deformations in which the particles or powders in the body rearrange. This is important in the technology of forming components from powders, and the theoretical understanding of certain phenomena is of practical importance (e.g. waves of densification encountered in non-stationary compacting). Other processes considered include cold compacting in a closed mould, the HIP process, and sintering in non-uniform temperature and stress fields. Simple models of real systems are employed so that the solutions are on the one hand explicit, and on the other hand, reflect real features induced by the compressibility of porous bodies. The interaction of external applied conditions and the internal densification caused by surface tension effects in sintering is examined, and the resulting model applied to sintering in non-uniform temperature and stress fields.