In this paper, we endeavour to give a numerical analysis of momentum and mass transfer characteristics in two viscoelastic fluid flows influenced by a porous stretching sheet, namely, second-grade and second-order non-Newtonian fluids by assigning both positive and negative values to the principal governing viscoelastic dimensionless parameter lambda(1). By means of suitable similarity transformations on the non-linear governing partial differential equations, we obtain several selected numerical solutions for non-dimensional concentration profiles and mass transfer characteristics. Graphs and tables are presented with a view to analyze the behaviour of the solution with changes in the governing dimensionless parameters of the problem. New results are obtained which show how the concentration distributions and mass transfer characteristics vary with suction/injection, viscoelasticity and magnetic field. Comparisons are given between the two aforementioned viscoelastic fluid flows and opposite trends with respect to the influence of viscoelasticity are observed. (c) 2007 Elsevier B.V. All rights reserved.