A new calculation procedure for the structural analysis of a free standing riser system is presented. The riser model includes a flexible jumper section and rigid riser section as two single continuous segments, which are coupled at the buoyancy can to form the overall riser static model. The equilibrium equations of the flexible jumper and rigid riser are established based on Minimum Total Potential Energy Principle. At each equilibrium configuration, the elastic potential energy of the system will be always equal to the sum of the potential energy caused by the external forces. The coupled equations are numerically solved by finite difference method, using Newton-Raphson technique in an iterative manner. This calculation procedure is evaluated by convergence analysis and the results validated by comparisons with well established commercial code. Parametric studies consider platform span, flexible jumper length, buoyancy force, buoyancy can depth and ocean current velocity effects to evaluate aspects related to simplicity, flexibility and robustness of the proposed methodology. The solution works as an expeditious alternative to enhance efficiency of the numerical calculations used in deep water riser design applications.