This paper discusses the mixed convection three-dimensional boundary layer flow of upper-convected Maxwell fluid over a stretching surface. Magnetohydrodynamic (MHD) combined with Soret and Dufour effects are also taken into account. The governing problems are first modeled and then solved by a homotopy analysis method (HAM). The variations of several parameters of interest on the velocity, concentration, and temperature fields are analyzed by the presentation of graphs. Several known results have been pointed out as the particular cases of the present analysis.