The kinematics of a flapping plate is determined by solving a path optimization problem for the hovering flight. The flapping motion of the flat plate is described by a combined sinusoidal plunging and pitching motion in the horizontal plane. The optimization process is carried out based on a well defined surrogate model which is made from the results of 2-dimensional computational fluid dynamics analysis. The Kriging method and genetic algorithm are utilized for the path optimization problem. The design variables are the pitching amplitude, the phase angles, and frequency of the flapping motion. The optimization results show that the drag force and the thrust force in the flapping motion cancel each other out because the flapping motion is almost symmetric. The lift force, which is almost the same as the weight of the flapping wing micro air vehicle, is only generated by the flapping motion.