This work focusses on deriving exact analytic solutions for an oscillatory flow of an elastico-viscous conducting fluid in a porous medium over a moving plate with variable suction. The momentum equation is enhanced with the resisting force offered by the permeability of the medium by incorporating the Darcy model. The energy transfer is equipped with volumetric heat generation/absorption and thermal radiation. Exact solutions for the governing equations are obtained by employing Cardan’s method, and comparative discussion is made by using the perturbation technique. The temperature distribution is evaluated by solving the energy equation considering relaxation time. Solutions of velocity fields are obtained for any value of viscoelastic parameter k$_1$. The results obtained from the analytical and approximation methods for any value of viscosity parameter are compared and found to be in good agreement. The physical behaviour of the pertinent parameters is obtained and displayed in graphs.