The goal of thesis is presentation of induction motor mathematical modeling method, which allows depending on problem to be solved definition to choose one of developed models for induction motor complicated dynamic regimes modeling and investigation. In the first chapter there is made analyze of existing induction motor mathematical models. There is presented induction motor mathematical model method on the base of two phase model in coordinate system x,y and developed a number of mathematical models for motor complicated dynamic regimes investigation. In the second chapter there are researched induction motor operation regimes which are not linked to switching like direct start-up, start-up taking into account current dislodgement in slots and operation at the voltage unbalance. In the third chapter there are researched induction motor operation regimes linked to switching like voltage brake on stator windings, switching over and self start. The forth chapter is devoted to problem of induction motor credible parameters definition for its dynamic regimes modeling.