At present, the majority of electric machine design software employs its own unique machine data structure. However, when users need to transfer their designs between software, they are often faced with significant obstacles or cannot obtain a parametric model suitable for optimization. In order to solve this issue, a universal parametric modeling framework is proposed for electric machine design. The geometric structure is strictly constrained to ensure that the model will not interfere with each part because of the randomness of input parameters. A data structure consisting of points, lines, and surfaces is constructed, and a conversion interface for parametric modeling with different software is established. Consequently, this universal framework can automatically generate parametric models appropriate for different finite element analysis (FEA) software according to the input parameters. The framework is especially convenient for users who need to design or optimize an electric machine, particularly when FEA software is required for verification. Numerical verification is performed using different software based on interior permanent magnet (IPM) synchronous machines to demonstrate the effectiveness of the framework.