The purpose of this study was to describe the application of 3D finite element analysis to determine resultant stresses on the bone anchored fixed prosthesis, implants and supporting bone of the mandible according to fixture numbers and load conditions. 4 or 6 fixtures and the bone anchored fixed prosthesis were placed in 3D finite element mandibular arch model which represents an actual mandibular skull. A $45^{circ}$ diagonal load of 10㎏ was labiolingually applied in the center of the prosthesis(P1). A $45^{circ}$ diagonal load of 20㎏ was buccolingually applied at the location of the 10mm or 20mm cantilever posterior to the most distal implant(P2 or P3). The vertical distribution loads were applied to the superior surfaces of both the right and the left 20mm cantilevers(P4). In order that the boundary conditions of the structure were located to the mandibular ramus and angle, the distal bone plane was to totally fixed to prevent rigid body motion of the entire model. 3D finite element analysis was perfomed for stress distribution and deflection on implants and supporting bone using commercial software(ABAQUS program. for Sun-SPARC Workstation. The results were as follows : 1. In all conditions of load, the hightest tensile stresses were observed at the metal lates of prostheses. 2. The higher tensile stresses were observed at the diagonal loads rather than the vertical loads 3. 6-implants cases were more stable than 4-implants cases for decreasing bending and torque under diagonal load on the anterior of prosthesis. 4. From a biomechanical perspective, high stress developed at the metal plate of cantilever-to-the most distal implant junctions as a consequence of loads applied to the cantilever extension. 5. Under diagonal load on cantilever extension, the 6-implants cases had a tendency to reduce displacement and to increase the reaction force of supporting point due to increasing the bendign stiffness of the prosthesis than 4-implants cases. 6. Under diagonal load on cantilever extension, the case of 10mm long cantilever was more stable than that of 20mm long cnatilever in respect of stress distribution and displacement. 7. When the ends of 10mm or 20mm long cantilever were loaded, the higher tensile stress was observed at the second most distal implant rather than the first most distal implant. 8. The 6-implants cases were more favorable about prevention of screw loosening under repeated loadings because 6-implants cases had smaller deformation and 4-implants cases had larger deformation.