The mass transfer of unsteady two-dimensional flow of MHD non-Newtonian Maxwell fluid over a stretching surface in the presence of first order constructive/destructive chemical reaction is presented. Upper convected Maxwell (UCM) fluid model is used here to characterize the non-Newtonian behavior of the fluid. Using similarity solutions the governing partial differential equations are transformed to ordinary differential equations and are then solved numerically by shooting method. The flow field and mass transfer are significantly influenced by the governing parameters. The results show that fluid velocity initially decreases with increasing unsteadiness parameter (0 to 0.3) and concentration decreases significantly due to unsteadiness. The effect of increasing values of the Maxwell parameter (0 to 0.4) is to suppress the velocity field. The concentration is enhanced with increasing Maxwell parameter. The fluid velocity decreases with increasing magnetic parameter (0 to 0.3). DOI: http://dx.doi.org/10.3329/jname.v9i2.12541 Journal of Naval Architecture and Marine Engineering 9(2012) 123-133