The finite element method is a very powerful tool used to analyze a variety of problems in engineering. This thesis looks at the finite element method as a tool and several important modeling features of concern. A well known finite element software package, ANSYS, will be used to demonstrate a diverse number of its capabilities, and several procedures followed in solving a specific engineering problem. The subject matter involves a nonlinear contact analysis of a pressure vessel having a threaded closure. The choice of this application is prompted by an interest in better understanding how the finite element method is implemented in the design and analysis of different pressure vessel parameters. A parametric finite element analysis was performed. Load and stress distributions along the threaded region of the vessel were examined for parameters including number of threads, thread pitch, diameter ratio, closure plug length, and thread profile.