The drilling process based on Material Reduction Rate (MRR) is modeled in this work. The modeling of this process is rather time-consuming and expensive as it involves 32 experiments with appropriate apparatus. Having had the model, the authors employed the well-known algorithm, namely Particle Swarm Optimization (PSO) to solve the maximization problem with some constraints present. All the results obtained showed non-violation to the constraints imposed. It means the solutions found are all feasible. The developed program may be useful for some practical purposes such as estimating the drilling duration, proper time to change the drill etc.