The present paper is concerned with the study of flow, heat and mass transfer characteristics in the unsteady free convective flow of an incompressible viscoelastic fluid over a moving vertical cone and a flat plate in the presence of magnetic field and higher order chemical reaction. The fluid viscosity and thermal conductivity are assumed to vary as a linear function of temperature. The governing partial differential equations are solved numerically using the implicit finite difference method of Crank-Nicolson type. The features of the fluid flow, heat and mass transfer characteristics are analyzed by plotting graphs and the physical aspects are discussed in detail. The results obtained show that the impact of magnetic field, buoyancy ratio parameter, viscosity variation parameter, Ecart number and chemical reaction parameter plays an important role in the viscoelastic fluid flow through porous medium. The mass transfer of the reactive species strongly depends on the chemical reaction parameter as well as the order of chemical reaction. (C) 2012 Elsevier Ltd. All rights reserved.