A Laplace transform is used to solve the problem of the steady state and transient response of a pinned head pile embedded into a viscoelastic Winkler soil medium. The pile is modeled as an Euler-Bernoulli beam while the soil medium is modeled using a Winkler subgrade approach. Two analytical solutions are developed to specifically address both steady state and transient loads encountered during dynamic pile testing. After choosing a proper contour integration in the complex plane, inverse integration is evaluated. The steady state solutions are associated to the residues of the integration around the poles while the transient solutions are associated to the integration paths along the contour integration. The derived solutions are applied to a case history for which results of dynamic pile tests are available. Dynamic pile flexion is generated by delivering eccentric impact using a dynamic loading test module. Validity of the proposed solution is discussed basing on geotechnical campaign and recorded pile head bending moment and rotation rate.