The transverse inertia effect considered and in terms of the principle of energy equilibrium in viscoelastic mechanics, the 6 order partial differential wave equation and universe solutions for the dimensionless relaxation and retardation time of wave propagation in simulated microbiology structures subjected to a uniaxial stress are deduced. The general solutions for the dimensionless relaxation and retardation time of wave propagation can converge to the classical results of Maxwell rheological model and Kelvin solid model separately when transverse inertia effect is not been taken into account. The transverse inertia effect leads to the increase of relaxation time of wave propagation with increasing Poisson ratio, ratio of diameter to wave length and layer number. The transverse inertia effect induces the decrease of retardation time of wave propagation with increasing Poisson ratio, ratio of diameter to wave length and layer number.