A model has been developed, based on the finite element method (FEM) of computational fluid dynamics (CFD), for the description of the complete flow field and concentration distribution inside a membrane capillary, driven in inside-out and dead-end or 'slow' cross-flow mode, sometimes referred to as 'bleed flow'. Particle or floc transport and deposition have been described by trajectory analysis, i.e. superimposing the calculation of forces and torques acting on the particles or flocs, based on the previously modelled fluid flow field. The model is used to give an overview of deposition behaviour and fouling layer formation of particles and flocs of a certain size in dead-end and cross-flow filtration. Example results are shown for different sized flocs. It is shown that the choice of dead-end or cross-flow operation is more significant if small floc aggregates have to be filtered by the membrane. Small flocs will be deposited more or less homogeneously along the membrane wall after some significant distance to the capillary inlet, leaving the first part of the membrane area unused for deposition. A 'Slow' cross-flow could be used to transport small flocs out of the capillary which entered the capillary cross section area in the neighbourhood of the axis. The faster the chosen cross-flow velocity, the larger the area. Larger flocs will be 'accumulated' in one resulting equilibrium trajectory and are transported to the rear end of the capillary, independent of their starting radial position at the inlet and operation conditions. It was calculated, that larger flocs will not be significantly transported out of the capillary lumen by introducing 'slow' cross-flow velocities at the capillaries outlet only.