  In classical mechanics, the motion of an object is described with Newton's
three laws of motion, which means that the motion of the material elements
composing a continuum can be described with the particle model. However, this
viewpoint is not objective, since the existence of transverse wave cannot be
predicted by the theory of elasticity based on the particle model. In this
paper, the material element of an elastomer is regarded as a rigid body, and
the traditional elastic wave equation is derived based on it. In the
derivation, the constitutive relations and strain-displacement relations are
correspondingly modified. The study reveals that the longitudinal and
transverse waves in elastomer correspond to the translational and rotational
motion of the material element, respectively. Besides, the reciprocity of shear
stress and shear strain is no longer requisite in continuum mechanics, and the
local rigid body rotation contributes stress.
