The transport of a particle-containing liquid through a capillary pore has been studied using a finite element method. Direct calculation has been made of flow fields, drag correction factors, and pressure drops for single particles and short chains of particles using the center-line approach. Three cases have been considered : a moving sphere in a stationary liquid, a stationary sphere in a moving liquid, and a moving sphere in a moving liquid. The correction factors for the inner sphere in short chains agree well with the results of complex stream function calculations for infinite chains of particles. Two topics have been particularly addressed. First covered is the use of the numerical calculations to identify the limiting particle spacings for which single-sphere calculations give close agreement with the calculations for such inner spheres. It is shown that single-sphere calculations have a wide range of applicability, considerably simplifying the effort involved in numerical calculation. Second, we carry out calculations up to large values of the particle radius/pore radius ratio. The case of a moving sphere in a moving liquid is directly relevant to the third topic of the paper-transport of particles through microfiltration membranes. Application of the numerical results for conditions corresponding to a commercial capillary pore microfiltration membrane show that hydrodynamic interactions can result in the maximum achievable flux for particle-containing fluids being significantly less than the pure water flux. Such hydrodynamic flux reduction has previously been neglected by membrane researchers.