This simulation employs Monte Carlo technique for studying fluid flow through a porous medium in the capillary regime. The medium has been modelled as a 2 or 3-dimensional network of elements, some of which are randomly closed to the fluid flow. Dijkstra's algorithm has been employed to identify the least-resistance pathway, which is instrumental in determining the minimum pressure required to achieve break-through across the network. At higher pressures, network resistance has been calculated by determining the manner in which the cluster forms and by accounting for the nature of flowpaths. The simulation yields a linear relationship between the pressure applied across the network and flowrate showing similarity to Darcy's law. Polynominal fitting of the data on the fraction of openable pores open as dependent on pressure applied across the network has been carried out and the coefficients determined.