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A dimensionless governing equation of clamped square plates was obtained by introducing dimensional analysis method to the basic governing equations of plates. The dimensionless governing equation includes three different influence aspects on structural dynamic response: the geometry of the structure, the dynamic resistance ability of material and the ratio of dynamic loads to the resistance ability of material. The dimensionless governing equation was applied to the dynamic response study of plates under blast loading, and a new dimensionless number was suggested for clamped square plates under explosion loads. The suggested dimensionless number has clear physical meaning, and the parameters included in the dimensionless number are easy to get. The dimensionless number suggested in this paper was applied to analysis the experimental data of clamped square plates under blast loading. Meanwhile, comparative analysis was proceeded which indicated the dimensionless number suggested in this paper can be effectively used to predict the dynamic response. The results showed the deflection-thickness ratio is in direct proportion to the dimensionless damage number. An empirical expression was obtained which can be used to the prediction of dynamic response of similar clamped plate under different blast loading condition.