This paper deals with a dynamic model for three-phase induction machines equipped with closed rotor slots and deep rotor bars. The thin bridges closing the rotor slots saturate highly as a function of the rotor current. The impedance of the rotor bars also varies much as a function of the rotor current frequency. An extended dynamic model, which takes into account the slot-bridge saturation and the deep-bar effect, is developed. The model extensions can be plugged into a standard machine model and parametrized easily. The proposed model can be applied to time-domain simulations, real-time control, and identification. The model is validated by means of finite-element analysis and experiments using a four-pole 5.6-kW induction machine. The results show that the accuracy of the proposed model is superior to the standard model, particularly under transient excitation typically used in standstill self-commissioning tests of induction motor drives.