Masticatory overload on dental implants is one of the causes of marginal bone resorption. The implant–abutment connection (IAC) design plays a critical role in the quality of the stress distribution, and, over the years, different designs were proposed. This study aimed to assess the mechanical behavior of three different types of IAC using a finite element model (FEM) analysis. Three types of two-piece implants were designed: two internal conical connection designs (models A and B) and one internal flat-to-flat connection design (model C). This three-dimensional analysis evaluated the response to static forces on the three models. The strain map, stress analysis, and safety factor were assessed by means of the FEM examination. The FEM analysis indicated that forces are transmitted on the abutment and implant’s neck in model B. In models A and C, forces were distributed along the internal screw, abutment areas, and implant’s neck. The stress distribution in model B showed a more homogeneous pattern, such that the peak forces were reduced. The conical shape of the head of the internal screw in model B seems to have a keystone role in transferring the forces at the surrounding structures. Further experiments should be carried out in order to confirm the present suppositions.