The Present Work deals with the most recent type of optimization algorithm known as Particle Swarm optimization and Matrix analysis of 3D Framed structures. As the science progresses, there is always a need of more fast, cheap and reliable method to meet our increasing demands. In field of optimization, PSO has achieved that. So, here we discuss the basic logics and algorithm behind this optimization technique with couple of examples showing how it works for simple mathematical problems and how it is better than other algorithms. Then, we frame a MATLAB program about 3D analysis of Framed structure using Matrix method. Then , we will see how the merging of two algorithms gives us the most optimum design of a frames structure with given loads applied.