The present contribution describes a CFD-based shape optimization study of an idealized bypass graft for the minimization of hemolysis under uncertain parameters. Bypass-grafts are implanted, in severe cases, to divert the blood around narrowed or occluded parts of an impaired artery. The unnatural hemodynamics induced by the flow diversion may lead to blood damaging phenomena, i.e. hemolysis. Significant efforts have been made to computationally estimate hemolysis and subsequently optimize the blood carrying geometries to reduce the hemolysis levels [1]. However, several parameters involved in the modeling of the problem have a certain level of ambiguity, as they result from studies in vitro or generally relate to stochastic biological phenomena. To this end and with respect to the sensitive nature of the application, a robust shape optimization, able to efficiently account for the uncertainties of the model, is required. We present several steady-state shape optimization studies accounting for uncertainties on (a) hemolysis modeling parameters, (b) non-Newtonian fluid parameters and (c) inflow boundary conditions. To this end, we also target to estimate the impact of each uncertain parameter on the optimization result. We employ a gradient-based approach relying on the first-order second-moment (FOSM) uncertainty quantification method. First-order gradients are efficiently computed with the assistance of an enhanced non-Newtonian adjoint technique [2]. The method is initially illustrated and verified through a 2D example with uncertain inflow. The 3D bypass-graft optimization results are additionally evaluated with respect to their uncertain quantification accuracy, using Monte Carlo simulations and in terms of their realistic application, using unsteady FSI simulations.