Finite element method (FEM) is preferred to carry out mechanical analyses for many complex biomechanical structures. For most of the biomechanical models such as oral and maxillofacial structures or patient-specific dental instruments, including nonlinearities, complicated geometries, complex material properties, or loading/boundary conditions, it is not possible to accomplish an analytical solution. The FEM is the most widely used numerical approach for such cases and found a wide range of application fields for investigating the biomechanical characteristics of oral and maxillofacial structures that are exposed to external forces or torques. The numerical results such as stress or strain distributions obtained from finite element analysis (FEA) enable dental researchers to evaluate the bone tissues subjected to the implant or prosthesis fixation from the viewpoint of (i) mechanical strength, (ii) material properties, (iii) geometry and dimensions, (iv) structural properties, (v) loading or boundary conditions, and (vi) quantity of implants or prostheses. This review paper evaluates the process of the FEA of the oral and maxillofacial structures step by step as followings: (i) a general perspective on the techniques for creating oral and maxillofacial models, (ii) definitions of material properties assigned to oral and maxillofacial tissues and related dental materials, (iii) definitions of contact types between tissue and dental instruments, (iv) details on loading and boundary conditions, and (v) meshing process.