Abstract: Theoretical and numerical solutions of the kinematics of table tennis are discussed in this paper. Under the general conditions of friction (sliding, rolling friction and air resistance), analytical solutions can be obtained only in limited conditions, but numerical solutions are universally available. This paper handles various numerical problems in solving the kinematics with Matlab, including using piecewise function,solving differential-algebraic equation, obtaining the interruption point of the integral equation, and verifying the accuracy of the numerical results through comparing with available analytical solutions. At last, two critical conditions are investigated, one for the determination of forward or backward motion of the ball, the other for the ball jumping back to the starting position.