In order to measure the strength of an agglomerated product it is convenient to compress a bed of the agglomerates using a piston in a rigid cylinder; this is known as a confined uniaxial compression test. A simple first-order lumped-parameter analysis of this compression process is presented, treating the system as purely dissipative and applying the Mohr-Coulomb macroscopic failure criterion. This enables average single agglomerate strengths to be deduced from the initial deformation behaviour of the bed under comparatively low loads. Agglomerates with a range of strengths have been formed from quartz sand using varying amounts of a polyvinylpyrrolidone binder. These have been tested both in the uniaxial compression test and individually, by compression between parallel platens. The results show agreement with the proposed theory over an order of magnitude in single particle crushing load. The load-deformation curve for the compression experiments is also consistent with Kawakita’s equation and it is shown that, over a certain range of strain, the load-deformation equation developed here and that due to Kawakita take approximately the same form; the agreement enables a physical interpretation to be made of one of the parameters in Kawakita’s equation.