We report the development of a computational model for the growth of multicellular tissues based on cellular automata to study the tissue growth rates and population dynamics of multiple populations of proliferating and migrating cells. Cell migration is modeled using a Markov chain approach and each population of cells has its own division and motion characteristics based on experimental data. The extended model contains a number of parameters that permits the study and analysis of cell population dynamics. This allows us to explore their effects on the overall tissue growth rate and the frequency of cell-cell interactions due to collision and aggregation. In addition to a sequential implementation, we developed a parallel algorithm and implemented it on a Beowulf Cluster using the Message Passing Interface. We present the sequential and parallel simulation results and analyze the performance of the parallel algorithm in terms of speedup and efficiency.