This study was designed to investigate the displacements and reaction forces of teeth caused by the application of the rectangular shape-memory arch wires with curve of Spee. Computer-aided three dimensional finite element method was adopted. This finite element model consists of brick element for teeth. beam element for the wire, and contact element for the periodontal ligament. And the applicaton of the MEAW(Multiloop Edgewise Arch Wire) was also studied so that the results of the two methods can be compared each other. Total number of the nodes and elements were found to be 5925 and 4031, repectively. In addition, several types of elastics and corresponding displacements and reaction forces were examined. The findings of this study were as follows: 1. When the rectangular shape-memory arch wire with curve of Spee was used alone, the intrusion and labioversion was noticeable on the upper incisors, while the upper molars showed less intrusion. With MEAW, the intrusion and labioversion of the upper incisors were slightly larger than those when the shape-memory arch wire was used, but on the upper molars the opposite result was obtained with respect to the intrusion. 2. The shape-memory arch wire with the vertical elastics caused the larger downward displacement on the upper canine than that when the MEAW was used with the vertical elastics. However, the downward displacement of the upper incisors was larger in MEAW. The uprighting and buccoversion of the molars were observed in both cases. 3. The use of the Class II or III elastics showed the extrusion and changes in torque of the corresponding teeth. The downward displacement of the upper canine was increased when the Class II and vertical elastics were applied simultaneously, but it was decreased when both of the Class III and vertical elastics were used.