The strain hardening of blends of polystyrene (PS) and ultra-high molecular weight polystyrene (UHMW-PS) in elongational flow is modeled by the molecular stress function (MSF) theory. Assuming that the ratios of strain energies stored in polydisperse and monodisperse polymers are identical for linear and nonlinear deformations, the value of the only non-linear parameter of the theory in extensional flows, the maximum molecular stress f(max), can be determined and is shown to be related to steady-state compliance J(e0). Using only linear-viscoelastic data, the elongational viscosity of PS/UHMW-PS blends is consistently predicted by the MSF theory.