The purpose of this study was to analyze how the stability of the implant prostheses and the loosening of the fastening screw was affected when the various types of Hex structure provided for the effect of anti-rotation of the single prostheses were given. Three dimensional finite element model was designed with which the implants with the external hex type of 0.75mm, 1.5mm and the implant with the internal hex type of 0.75mm, 1.5mm and the implant with the external hex type of $15^{circ}$ tapered shape of 0.75mm were supposed to completely osseointegrate to the mandible. After fininshing the finite element model, the preload of 10N at the fastening screw was applied and then the vertical and $30^{circ}$ lateral load of 200N was applied respectively at the cusp tips of the prostheses. The following results were obtained : 1. In case of displacement, the amount of displacement was increased at the internal hex type(model C, D) than at the external hex type(model A, B, E) when the vertical and lateral load was applied. 2. Less equivalent stress was represented at the model B with increased external hex height than at the model A when the vertical and lateral load was applied. 3. Much stress was represented at the model E with increased hex angle than at the model A in case of the stress happened to the implant body and the fastening screw when the vertical and lateral load was applied. 4. Much equivalent stress was represented at the model D with deepened internal hex height than at the model C when vertical and lateral load was applied. 5. The least stress was taken at the model B and the most stress was taken at the model D in case of the stress happened to the implant when the vertical and lateral load was applied. 6. The least stress was taken at the model C at the vertical load. And the least stress was taken at the model B at lateral load in case of the stress happened to the fastening screw. As a results of this study, the good lateral stability of prostheses and less stress of the component of implant was taken when the external hex height was increased, and the risk of neck fracture of implant and fastening screw was increased when the internal hex height was deepned because of long screw neck portion and thin implant neck portion.