Many pressure-volume relationships for powders under confined uniaxial compression have been proposed. However, they are essentially empirical in origin with the exception of the lumped parameter relationship developed in previous work. In the current study, it is shown that either the latter relationship or that due to Kawakita, Powder Technol., 74 (1970/71) 61, may be employed to determine the tensile strength of agglomerates provided that the influence of the friction at the wall of the compaction cell is taken into account. A micromechanical model of powder compaction is proposed which leads to an explicit form of the Kawakita relationship. It is shown that for particles which deform plastically, rather than fracture, the compaction behaviour may be described by a reduced form of this explicit relationship. The micromechanical modelling is based upon the affine deformation of particles in load carrying chains or columns such that particles between the chains are redundant with respect to the load carrying capacity.