This thesis paper examines the feasibility of using external-beam PIXE to study the surface enrichment effect in metal artifacts. By varying the energy of the incident proton beam, we penetrated the artifact's surface to different levels and were able to produce a depth profile of the elemental composition of the sample. In this study, the sample set we chose to examine consisted of ancient and modern coins. This paper first describes the surface enrichment effect and theoretically how PIXE can be used to study it. It then details the construction of the components of the external-beam setup. Many of the refinements of the hardware and experimental methods are discussed. It recounts the means of calibration of the detector and analytical tools. Finally, an accounting of the research performed on several coins is set forth, along with data showing the effectiveness of PIXE in complementing other methods of elemental analysis. We found that PIXE revealed statistically significant differences in concentrations of modern coins at the two beam energies we used. Ancient coins did not have similarly significant discrepancies between the two beam energies. The modern coin data suggested depletion in copper in copper-silver and copper-gold alloys, which is consistent with predictions of the theory of the surface enrichment effect. We suggest that the ancient coins are so deeply corroded that the PIXE beam is unable to penetrate adequately to observe surface enrichment. Comparison of our PIXE data to XRF and SEM data suggest that the trends we observed in modern coins are verified by the other methods. We therefore assert that external-beam PIXE is an effective tool for studying the surface enrichment effect, though with the beam energies available at Brigham Young University, the study must be limited to fairly modern coins.