During the past decade there has been a tremendous surge in understanding the nature of parallel computation. A number of parallel computers are commercially available. However, there are some problems in developing application programs on these computers;This dissertation considers various issues involved in implementing parallel algorithms on Multiple Instruction Multiple Data (MIMD) machines with a bounded number of processors. Strategies for implementing divide-and-conquer algorithms on MIMD machines are proposed. Results linking time complexity, communication complexity and the complexity of divide-and-combine functions of divide-and-conquer algorithms are analyzed. An efficient criterion for partitioning a parallel program is proposed and a method for obtaining a closed form expression for time complexity of a parallel program in terms of problem size and number of processors is developed.