Abstract: The equivalent characteristic constitutive equations were founded in this paper. Based on the classic composites laminates theory , the stiffness mat rix and the equivalent damping mat rix of the laminates which can be described by elastic constant s and damping constant s were determined. The explicit relationship between elastic constant s and the mode was determined , as well as the explicit relationship between damping constant s and the mode.The equivalent damping mat rix of any laminates can be easily calculated out when the equivalent damping constant sin the constitutive equations are identified. The validity of this method is demonst rated through numerical examples.