This work considers free‐flexural vibrations of a free‐elliptical plate by the use of Mathieu functions and modified Mathieu functions which are solutions of the differential equation of motion and by the method leading to the frequency equation by making use of orthogonal property of Mathieu functions. The non‐dimensional frequencies calculated numerically for the first five normal modes of symmetrical vibration about both axes are tabulated for various aspect ratios and are shown in graphs for the eccentricities. The experimental results are obtained and are found to be in good agreement with the theoretical results.