This paper introduces a mesh-based magnetic equivalent circuit (MEC) modeling technique for induction machines (IMs) in healthy and broken rotor bars conditions. The MEC model is presented as a highly accurate and computationally efficient alternative to finite element (FE) models. By incorporating modifications to the air gap coupling method, including a new Lagrange interpolation function, and utilizing a harmonic MEC model, the accuracy of the solution is improved while reducing electrical and mechanical transients. Compared to experiments and 2D FE models, this model achieves precise results for electromagnetic torque, rotational speed, and forces across various conditions. The Lagrange interpolation function forms the basis for the air gap coupling between stator and rotor flux densities. The results demonstrate the MEC model’s exceptional accuracy in predicting speed oscillations, calculating forces, and analyzing current harmonics in faulty IMs. Furthermore, the MEC model performs over 30 times faster than the 2D FE models.