Abstract: In practical engineering, rectangular thin plate structures with concentrated mass points or equivalent to concentrated mass points have a wide range of applications in mechanical engineering, electronic engineering, and vehicle engineering, such as supporting workbenches, ship decks, PCB boards and so on. The modified Fourier Ritz method is used to establish the numerical analysis model of rectangular thin plate with lumped mass under general boundary conditions, which can avoid the problems of non-derivability or discontinuity at the boundary of thin plates in traditional methods. In addition, the Fourier expansion in the form of cosine function plus polynomial has better convergence than that in the form of sine function. The calculation method of mass matrix and stiffness matrix of rectangular thin plate with concentrated mass is given, the parameters of different boundary constraints are analyzed, and the influence of the size, position and quantity of concentrated mass on the modal of rectangular plate is discussed. The method and its results can be applied to the vibration analysis and vibration control of rectangular thin plates.