In this paper we outline the theory behind a computer simulation of solder paste flowing out of a stencil aperture during printing for surface-mount technology (SMT) assembly. Although developed to deal with solder pastes, the techniques are applicable for any dense suspension satisfying certain conditions. The simulation is based on lubrication theory, and hence is valid when the gaps between particles are small. The motion of each particle in the paste is calculated from the forces exerted by nearest-neighbour particles and the walls, and the movement of each individual particle is tracked. We present here the theory, methods, assumptions, limitations and general applicability of the model. In Part II, we present the results of the model for the special case of solder paste withdrawing from a stencil aperture.