For static bending and free vibration problems of moderately thick plate, by introducing two auxiliary functions and using the differential equations and the boundary conditions based on Reisser plate theory presented by Hu Hai-chang, the governing equations were introduced into Hamilton system, and the differential equation set model of static bending and free vibration problems of moderately thick plate were presented respectively. The unitary model for the two problems was given after comparison. In the presented united forms, the Hamilton matrix H includes two zero block matrix in the diagonal place. For the homogeneous differential equation set, the characteristic roots were compared for the static bending and free vibration problems of moderately thick plate. Then the ordinary solutions of the homogeneous equations were obtained and compared. Thus the solution finding is rational and reasonable. The solving procedure follows a set of methodology,and the solving procedure can be extended to other problems.