The distribution of stress in the jawbone during mastication is highlighted in this paper as an important index of the mechanical performance of dental implants. The objective of this paper is twofold. The first objective was to demonstrate the importance of considering the heterogeneity (spatial distribution) of the mechanical properties of jawbone in stress analysis. Next, the influence of the alignments of the implants on the peri-implant bone stress was examined using a finite element method (FEM) and numerical analysis model which reproduced the heterogeneity of the jawbone based on the spatial distribution of the bone density measured as CT data. For the former objective, numerical analyses of a finite element model of the mandible of a patient were conducted. Using CT data of this patient and taking into account the non-uniformity (spatial distribution) of bone density, we reproduced a patient-specific geometry and mechanical properties of the jawbone. In-vivo three-dimensional loads measured by instruments attached to the implants were used in the numerical analyses. As for the material properties of jawbone, we employed two models: a multi-value model that considers the inhomogeneity and spatial variability of mechanical properties of the bone, and a binary model with two discrete mechanical properties for cortical bone and cancellous bone. In the numerical analyses, a large difference in the stress distributions was observed between these two models. This demonstrates the insufficiency of the over-simplified binary model and the validity of the multi-value model that is closer to reality. The effects of the alignments of the implants were analyzed against the maximal voluntary clenching (MVC) load measured in the patient. As a result, peri-implant bone stress was found to be greatly reduced when the alignments of the implants were changed to match the direction of MVC load. It is suggested that such alignments are optimal. As more realistic loads, the loads measured while chewing peanuts were used for implants aligned in such optimal directions. For those loads, stress reduction was observed, especially when the loads had large magnitudes. Thus, we demonstrated the importance of accurate modeling of bone material properties and the alignments of implants in terms of the distribution of peri-implant bone stress.