The project involved developing a mathematical model of machining teeth of a spiral bevel gear and a mathematical model of the gear pair . The mathematical model of machining was based on generative machining with a single indexing system (face milling). On the basis of tool geometry, technological settings, kinematics of the process based on the vector and matrix calculus and differential machining geometry, a tooth model was built and tooth surfaces were obtained. The mathematical model of the gear pair was developed with the use of the gear geometry and the obtained tooth surfaces of the pinion and the gear. The model allows for the possibility of introducing errors due to gear settings and tolerances of the manufacturing errors in housings and other transmission components. The mathematical model of the gear pair was used to obtain the contact pattern and the transmission error graph. An analysis of the results and the pplication of meshing quality indicators allowed us to improve the gear transmission. This process was carried out in an iterative cycle by changing the set-up (by modifying technological machining) parameters of the machined surfaces of the teeth. The application of both models, i.e. the mathematical model of machining teeth of a spiral bevel gear and a mathematical model of the gear pair, was presented using the example of aircraft gear 18:43.