Since their conception in the 1960s, panel codes have remained a critical tool in the design and development of air vehicles. With continued advancement in computational technologies, today's codes are able to solve flow fields around arbitrary bodies more quickly and with higher fidelity than those that preceded them. Panel codes prove most useful during the conceptual design phase of an air vehicle, allowing engineers to iterate designs, and generate full solutions of the flow field around a vehicle in a matter of seconds to minutes instead of hours to days using traditional CFD methods. There have been relatively few panel codes with the capacity to solve supersonic flow fields, and there has been little recently published work done to improve upon them. This work implements supersonic potential flow methods into Cal Poly’s open source panel code, CPanel. CPanel was originally developed to solve steady, subsonic flows utilizing constant strength source and doublet panels to define the geometry, and an unstructured geometry discretization; it was later extended to include viscous vortex particle wakes and transient modeling. In this thesis, a higher-order method is implemented in CPanel for use in solving linearized supersonic flows, where a higher-order method is one that utilizes at least one singularity element whose order is higher than constant. CPanel results are verified against analytical solutions, such as the Taylor-Maccoll solution for supersonic conical flows and 2D shock-expansion theory, and the PANAIR and MARCAP supersonic panel codes. Results correlate well with the analytical solutions, and show strong agreement with the other codes.