This thesis covers three aspects of Microstrip antenna designs. The first is the analysis and design of single element rectangular Microstrip antenna which operates at the central frequency of 2.4 GHz and the second aspect is the design of dual band rectangular Microstrip antenna which is operates as 2.4 & 3.08 GHz. Both antennas have been modeled, designed and simulated. The simulation process has been done through IE3D electromagnetic software which is based on method of movement (MOM). The third is the interfacing between IE3D/PSO (MATLAB). In this part optimization is done through Particle Swarm Optimization (PSO) algorithm using IE3D simulation software. The technique has proven successful for many electromagnetic problems and is a robust and stochastic search method.