<p>Functionally graded materials (FGMs) are widely used in engineering due to their superior mechanical properties. However, their impact behavior is typically studied through numerical simulations or experimental methods, which are often time-consuming and resource-intensive. In this study, we investigate the impact response of a two-phase functionally graded plate by establishing the governing equations based on the Zener model and a modified Hertz contact law. Compared with prior studies relying on numerical or experimental techniques, this analytical approach offers a more efficient and cost-effective tool. This study is the first to extend the homotopy method—previously applied to homogeneous plates—to derive analytical solutions for functionally graded plates under impact. From the analytical solution, we derive explicit expressions for the maximum impact force, maximum impact depth, total contact time, total compression time, and the coefficient of restitution. These expressions enable us to analyze the influence of the functionally graded index, as well as the ratios of elastic modulus and density between the top and bottom surfaces of the plate during the impact process. The results quantitatively explain the superior performance of functionally graded plates and determine the optimal functionally graded index corresponding to the maximum coefficient of recovery.</p>