The issue of dental implant placement relative to the alveolar crest, whether in supracrestal, equicrestal, or subcrestal positions, remains highly controversial, leading to conflicting data in various studies. Three-dimensional (3D) Finite Element Analysis (FEA) can offer insights into the biomechanical aspects of dental implants and the surrounding bone. A 3D model of the jaw was generated using computed tomography (CT) scans, considering a cortical thickness of 1.5 mm. Subsequently, Morse cone implant–abutment connection implants were virtually positioned at the model’s center, at equicrestal (0 mm) and subcrestal levels (−1 mm and −2 mm). The findings indicated the highest stress within the cortical bone around the equicrestally placed implant, the lowest stress in the −2 mm subcrestally placed implant, and intermediate stresses in the −1 mm subcrestally placed implant. In terms of clinical relevance, this study suggested that subcrestal placement of a Morse cone implant–abutment connection (ranging between −1 and −2 mm) could be recommended to reduce peri-implant bone resorption and achieve longer-term implant success.