The component method is proposed to study the free vibration of a multispan Mindlin plate. The orthogonality of any two distinct sets of the mode shape functions is shown. A method of modal analysis is then presented to study the dynamic responses of the plates. A line load moving on the plate is used as an example. The effects of span number, rotatory intertia and transverse shear deformation on the critical velocity, the maximum displacement and the maximum moment of plates are discussed. Furthermore, the effect of the thickness‐length ratio on the critical velocity is also investigated. The results of a Mindlin plate are compared with those of a classical plate.