The paper describes flow behavior simulation of polymer melt in cavities of injection molds to clarify the relationship between flow behavior and mold shapes under several injection conditions. It uses FEM ; the governing equations are Stokes equation, equation of continuity and of heat conduction. Temperature in the flowing polymer melt in a mold varies spatially and temporally during injection molding process. The former is considered in finite partitioning of the unisothermal region by means of Tridiagonalized Partition Method (Zienkiewicz, 1967), the latter in the respective FEM analysis for flow and for heat repeated alternatively by the same time increment. In comparing the results of analysis with the experiment (Short-Shot Method), the analysis shows that the simulation is useful as a prediction of melt-front shape in the process and a generating position of weld-line, but quantitatively agrees not well with the experiment in the arrival time and temperature of melt-front, because of including no generating heat inside of flowing melt.