Cable stayed bridges have good stability, optimum use of structural materials, aesthetic, relatively low design and maintenance costs, and efficient structural characteristics. Therefore, this type of bridges are becoming more and more popular and are usually preferred for long span crossings compared to suspension bridges. A cable-stayed bridge consists of one or more towers with cables supporting the bridge deck. In terms of cable arrangements, the most common type of cable stayed bridges are fan, harp, and semi fan bridges. Because of their large size and nonlinear structural behaviour, the analysis of these types of bridges is more complicated than conventional bridges. In these bridges, the cables are the main source of nonlinearity. Obtaining the optimum distribution of post-tensioning cable forces is an important task and plays a major role in optimizing the design of cable stayed bridges. An optimum design of a cable-stayed bridge with minimum cost while achieving strength and serviceability requirements is a challenging task. In this thesis, an advanced and comprehensive numerical model is used to obtain the post-tensioning forces and the optimum design of the three types of cable-stayed bridge. The numerical method is based on finite element, B-spline curves, and real coded genetic algorithm. The optimization accounts for all the variables that define the geometry and cross-section of the bridge. Comparison between the three types, in terms of post-tensioning forces and cost, is carried out in this thesis