An improved mathematical model with the attendant computer program to calculate multiphase fluid flow in petroleum reservoirs is presented. The model is used to simulate the behavior when a fluid is used to displace hydrocarbon fluids in a reservoir. The method is an expansion of a previously published method, in Bureau of Mines ri 7011, but handles constant injection rate as an alternative to constant pressure. Program documentation is provided along with thorough explanations of the added program features. Using the program, the petroleum engineer can calculate oil recoveries for different flood patterns and operating conditions and select the conditions most likely to optimize recovery. Experience with the previous model demonstrated the need for the improvements in order to simulate reservoir behavior more accurately. The improved method will result in improved oil recovery. In this paper, the significant improvements are described in detail so that anyone interested can put the program to use.