This thesis aims to study different analytical methods to model a squirrel cage induction motor, which should have minimal simulation time than the corresponding finite element method (FEM) based models. The purpose of doing so is to develop a model suitable to simulate all major faults and be used for advanced model-dependent fault diagnostic algorithms, such as parameters estimation and inverse problem theory. This thesis's second key objective is to study various signal-processing techniques for their pros and cons to detect fault at the embryonic stage and investigate the entire current harmonic spectrum of induction motors both in transient and steady-state regions. Thus, the motor under healthy and broken rotor bar (BRB) conditions are simulated, and experimental measurements are investigated for validation.The dynamic d-q model with the inclusion of non-linear magnetization inductance was considered as a starting point. This model helps understand the machine's basic concepts because of its comprehensiveness and ability to produce compact equations, which can be used for drives as general and in observers and state estimators as particular. However, this model was found to be less suitable to simulate machine faults because of the considered approximations.To address the d-q model limitations, the winding function analysis (WFA) based model was prepared. In this model, the analytical equations to calculate various inductances, resistances, currents, fluxes, torque, and speed are derived for the motor under investigation. These equations were simulated in MATLAB, giving results near to the practical measurements. The model is suitable for implementing some faults, such as BRB and broken end rings. Still, the consideration of constant air gap makes it less ideal for the implementation of eccentricity and saturation-related faults. Moreover, the spatial harmonics, which are very important for fault diagnostics and sensor-less speed estimation, cannot be simulated. Those approximations can be reduced with Fourier summation of higher-order harmonics (winding) and Taylor series to include inverse air gap functions but at the cost of the self-defined number and amplitude of harmonics.To get more realistic results, the modified winding function analysis (MWFA) based model was prepared to ensure that all winding functions and air gap were defined as a function of stator and rotor individual and respective angles. The geometry of stator and rotor slots is considered to calculate the leakage inductances and various resistances. The self and mutual inductances