Based on Reddy’s layerwise theory, the governing equations for dynamic response of viscoelastic laminated plate are derived by using the quadratic interpolation function for displacement in the direction of plate thickness. Vibration frequencies and loss factors are calculated for free vibration of simply supported viscoelastic sandwich plate, showing good agreement with the results in the literature. Harmonious transverse stresses can be obtained. The results show that the transverse shear stresses are the main factor to the delamination of viscoelastic laminated plate in lower-frequency free vibration, and the transverse normal stress is the main one in higher-frequency free vibration. Relationship between the modulus of viscoelastic materials and transverse stress is analyzed. Ratio between the transverse stress’s maximum value and the in-plane stress’s maximum-value is obtained. The results show that the proposed method, and the adopted equations and programs are reliable. Based on Reddy's layerwise theory, the governing equations for dynamic response of viscoelastic laminated plates are derived by using the quadratic interpolation function for displacement in the direction of plate thickness. Vibration frequencies and loss factors are calculated for free vibration of simply supported viscoelastic sandwich plates, showing results agree with the results in the literature. Harmonized transverse stresses can be obtained. The results show that the transverse shear stresses are the main factor to the delamination of viscoelastic laminated plates in lower-frequency free vibration, and the transverse normal stress is the main one in higher-frequency free vibration. The relationship between the modulus of viscoelastic materials and transverse stress is analyzed. Ratio between the transverse stress's maximum value and the in-plane stress's maximum-value is obtained. the adopted equations and programs are reliable.