The use of hollow-fibre membranes for microfiltration introduces trans-membrane pressure gradients that have important implications for flux decline mechanisms. A model is developed to elucidate these mechanisms for typical hollow-fibre membranes during the dead-end microfiltration of particulate suspensions. The model accommodates both compressible and incompressible cakes, and predicts highly-localised fluxes which are completely absent in planar membranes. These localised fluxes combine with trans-membrane pressure gradients to produce non-uniform cake growth patterns and non-uniform cake resistance profiles. When a cake is moderately compressible, the permeate flux declines through the axial motion of a uniform flux front. When a cake is highly compressible, the flux declines through the axial motion of a localised flux zone which leaves a low-permeability cake in its wake. Cake growth patterns are non-uniform in both axial and transverse directions. However, after substantial flux decline, a uniform cake growth pattern is established and thereafter the hollow fibre filters like a planar membrane. These flux decline mechanisms produce permeate flux declines with throughput which depend on hollow-fibre aspect ratio and permeability in addition to the properties of the retained cake.