Slow squeeze flow of a paste between two parallel circular discs of radius R is considered. A previous analysis [J.D. Sherwood, Liquid-solid relative motion during squeeze flow of pastes, J. Non-Newtonian Fluid Mech. 104 (2002) 1-32] predicts that the solids volume fraction within the paste becomes very non-uniform, with a high solids volume fraction near the axis of the two discs. If squeezing is so slow that the liquid within the paste has ample time to move relative to the particles, the liquid pressure within the paste remains close to uniform. This limit is considered in detail. The matrix of particles within a central region r < r(1) (h) near the axis compacts uniaxially. The wall shear stress in this central region is insufficient for the matrix of particles to slip at the wall, and only liquid is squeezed outwards. In the outer region r > r(1) particles and liquid move radially outwards, though at different velocities. Initially r(1) = R, but the central region of unixial compaction shrinks and eventually vanishes. If the initial solids volume fraction of the paste is low, the matrix of solid particles in the paste is very compressible and uniaxial compaction plays a major role in the early stages of compression. Numerical analysis is then required in order to follow the compaction history of the paste. (c) 2005 Elsevier B.V. All rights reserved.