Purpose: Four finite element models were constructed in the mandible having a single implant fixture connected to the first premolar-shaped superstructure, in order to evaluate how the shape of the fixture and the implant-abutment connection would influence the stress level of the supporting tissues fixtures, and prosthethic components. Material and methods : The superstructures were constructed using UCLA type abutment, ADA type III gold alloy was used to fabricate a crown and then connected to the fixture with an abutment screw. The models BRA, END , FRI, ITI were constructed from the mandible implanted with Branemark, Endopore, Frialit-2, I.T.I. systems respectively. In each model, 150 N of vertical load was placed on the central pit of an occlusal plane and 150 N of $40^{circ}$ oblique load was placed on the buccal cusp. The displacement and stress distribution in the supporting tissues and the other components were analysed using a 2-dimensional finite element analysis . The maximum stress in each reference area was compared. Results : 1. Under $40^{circ}$ oblique loading, the maximum stress was larger in the implant, superstructure and supporting tissue, compared to the stress pattern under vertical loading. 2. In the implant, prosthesis and supporting tissue, the maximum stress was smaller with the internal connection type (FRI) and the morse taper type (ITI) when compared to that of the external connection type (BRA & END). 3. In the superstructure and implant/abutment interface, the maximum stress was smaller with the internal connection type (FRI) and the morse taper type (ITI) when compared to that of the external connection type (BRA & END). 4. In the implant fixture, the maximum stress was smaller with the internal connection type (FRI) and the morse taper type (ITI) when compared to that of the external connection type (BRA & END). 5 The stress was more evenly distributed in the bone/implant interface through the FRI of trapezoidal step design. Especially Under $40^{circ}$ oblique loading, The maximum stress was smallest in the bone/implant interface. 6. In the implant and superstructure and supporting tissue, the maximum stress occured at the crown loading point through the ITI. Conclusion: The stress distribution of the supporting tissue was affected by shape of a fixture and implant-abutment connection. The magnitude of maximum stress was reduced with the internal connection type (FRI) and the morse taper type (ITI) in the implant, prosthesis and supporting tissue. Trapezoidal step design of FRI showed evenly distributed the stress at the bone/implant interface.