In this paper we analyze the non-integrability of the Wilbeforcespring-pendulum by means of Morales-Ramis theory in where is enough to provethat the Galois group of the variational equation is not virtuallyabelian. We obtain these non-integrability results due to thealgebrization of the variational equation falls into a Heundifferential equation with four singularities and then we applyKovacic's algorithm to determine its non-integrability.