The influence of radiation on the unsteady MHD free convection Viscoelastic fluid flow past an exponentially accelerated moving vertical plate through porous medium with chemical reaction is investigated theoretically. The fluid considered here is a gray, absorbing-emitting radiation but non-scattering medium, and the Boussinesq’s approximation is considered for pressure gradient in momentum equation and Taylor’s series expansion to describe the radiative heat flux in the energy equation. The dimensionless governing partial differential equations are solved using Laplace transform technique. They satisfy all imposed initial and boundary conditions and for S→ 0 can be reduce to the similar solutions for Newtonian fluids. The corresponding expressions for skin friction, Nusselt number and Sherwood number also evaluated. Numerical results for velocity, temperature and concentration are shown graphically. This study is of fundamental importance and frequently arises in many practical situations such as chemical engineering and polymer extrusion processes. The effect of different parameters like thermal radiation parameter, visco-elastic parameter, chemical reaction parameter, magnetic field parameter, permeability parameter, Schmidt number and Prandtl number are discussed. It is observed that the momentum and thermal boundary layer thickness decreases owing to an increase in the value of the radiation parameter. An increase in the Prandtl number is found to decrease the velocity and temperature but increasing in Nusselt number for air and water. © 2017, Springer India Pvt. Ltd.