This study evaluates the impact of integrating Phase Change Materials (PCMs) in the efficiency of Ground-Air Heat Exchangers (GAHEs). A three-dimensional computational model for the GAHE system with an integrated annular PCM (GAHE-PCM) was implemented in ANSYS Fluent using the Finite Volume Method, accounting for the meteorological conditions and ground properties of Viamão, Brazil. A parametric evaluation with fifteen rectangular and fifteen elliptical PCM container configurations were analyzed by varying their geometric ratios. Results indicate that the inclusion of PCM may enhance the yearly thermal potential as high as 69.31% in heating and 27.92% in cooling. Geometries, such as square or circular cross-sections, maximize heat exchange with the airflow, whereas elongated shapes reduce PCM efficiency. Furthermore, placing most of the PCM in deeper, thermally stable soil layers reduces the overall performance. For near-optimal designs, the differences between rectangular and elliptical containers are minimal, providing flexibility for system implementation.