A cylinder of height it is squeezed between two parallel circular plates of radius R much greater than h. The cylinder is assumed to behave as a generalised Newtonian material in which the stress and strain rate are coaxial: the particular cases of a rigid-plastic solid and power-law fluid are considered in detail. It is assumed that the frictional stress at the walls is a fixed fraction m of the yield stress in shear, k, in the case of the plastic material, and a fixed fraction of the effective Mises stress in the case of the power-law fluid. This boundary condition, often used in plasticity analysis, leads in both cases to a constant shear stress at the walls, rather than a no-slip boundary condition. Hoop stresses are included in an approximate analysis in which stresses and velocities are expanded as series in inverse powers of the radial coordinate r: these expansions break down near the axis r = 0 of the cylinder. The force required to compress the rigid-plastic cylinder is F = 2/3mk pi R(3)h(-1) + 1/2 root 3k pi R(2)[(l - m(2))(1/2) + m(-1) sin(-1) m] + O(kRh), independent of the speed of compression. The analysis can be extended to other solids and fluids characterised by a coaxial constitutive relation: by way of example, results are presented for the Bingham fluid.