The dynamic analysis of cracked thin rectangular plates subjected to a moving mass, first is investigated in this paper. To this end, the eigenfunction expansion method is utilized to solve the ruling differential equation of motion. For the first time, intact plate orthogonal polynomials, in the combination with the well-known corner functions, as a composition, are employed in the governing equation, required the professional computer programming, to solve the equation. The proposed solutions, afford upper bounds for the true solutions, which is a property of an appropriate numerical solution. Parametric investigations, are performed to determine, effects of moving mass weights, moving mass velocities, crack lengths, crack angular orientations, and plates' aspect ratios, on dynamic responses of cracked thin rectangular plates. The results confirm, that the moving mass, has a greater impact, than the moving load on dynamic responses of cracked thin rectangular plates. Furthermore, there are non-monotonous nonlinear relations, between altering dynamic responses of cracked thin rectangular plates with various boundary conditions, and modifying moving mass weights, moving mass velocities, crack lengths, inclined crack angles, as well as plates' aspect ratios respectively.