This paper describes an algorithm for simulating matrix fractured reservoirs. Response curves for individual matrix blocks developed by numerically simulating the inhibition processes in individual blocks for several sets of boundary conditions are coupled in an iterative process to describe vertical water movement and oil production in the simulator. This simulator can be used to estimate the efficiency of waterflooding in matrix fractured reservoirs as a function of reservoir and matrix block description and planned waterflooding rates. The simulator has been used on an example reservoir to develop some general results and conclusions. For matrix fractured reservoirs, ultimate recoveries will be greater if there are relative few blocks in the vertical direction and flooding rates are kept low. If individual blocks are tall and flooding rates are high low recoveries can be expected. The water oil ratio increases more rapidly in matrix fractured reservoirs after water breakthrough than in homogeneous reservoirs.