High speed squirrel-cage motors are a relatively unknown group of machines, mainly due to their particular application. High rotational speed is achieved by supplying the motors with 400-1500Hz frequency voltage. Their operation in special conditions results in the fact that their structure and some properties differ from those of squirrel-cage induction machines supplied with 50Hz frequency voltage. The use of closed rotor slots causes strong saturation of the magnetic circuit for the slot leakage flux. Changes in the current in the slot causes a varying state of saturation and thus rotor leakage inductance is not a constant parameter. When determining the rotor winding leakage inductance for classic induction motors supplied with 50Hz frequency voltage, the influence of the saturation of the magnetic circuit for the leakage flux is usually omitted. This is a standard approach and an equivalent scheme, mentioned in literature, is used in such a case. Identification of the inductance in motors supplied with high frequency voltage, in which the phenomenon of core saturation occurs, is a relatively complex issue due to the complicated distribution of magnetic flux, and especially the leakage flux. The value of leakage inductance was determined experimentally. The paper presents differential equations describing a mathematical model and transients of the current and electromagnetic torque, obtained by simulating the start-up of a squirrel-cage high-speed motor.