Based on the time histories of stress and strain of the sole under metatarsal heads during the loading and unloading process, we propose an appropriate, nonlinear, viscoelastic model that describes probably the constitutive law for that soft tissue. We use the technique of optimization to find the parameters in the equation of the constitutive law that fit best the experimental data. By varying the strain waveform, we can derive theoretically the explicit equation expressing the relation between the energy dissipation and the parameters of the constitutive law. Besides the stress and strain analysis, we have also done the vibration analysis of the sole’s soft tissue. We use Hamilton’s principle to derive the equations of vibration of the sole’s soft tissue. The effects of the parameters in constitutive law and the geometric size of the soft tissue on the frequency shift and amplitude change are studied.