Mathematical Programs with Vanishing Constraints (MPVC) form a class of constrained optimization problems characterized by constraints that may become inactive or redundant at certain feasible points. In this chapter, we investigate the application of Particle Swarm Optimization (PSO) to solve both smooth and nonsmooth MPVC problems. PSO is a population-based metaheuristic inspired by the social behavior observed in bird flocks and fish schools. It is particularly effective for addressing complex, nonlinear, nonconvex, and combinatorial optimization problems encountered in various scientific and engineering domains. Furthermore, the method is capable of handling problems with unbounded constraint sets whose solutions are located at finite points. To handle the constraints inherent in MPVC problems, a penalty function approach is incorporated into the PSO framework. The performance of the proposed method is assessed using a set of 10 test problems from the literature, each with a known optimal solution. For each test case, 20 independent runs of the PSO algorithm were carried out to evaluate its consistency and robustness. The results show that the algorithm consistently converges to solutions very close to the known optima, demonstrating its effectiveness, reliability, and suitability for solving MPVC problems.