A new lattice-Boltzmann finite-element method is used to simulate large numbers of deformable red blood cells and platelets in suspension for the investigation of stress-mediated platelet-deposition mechanisms in blood. The coupled lattice-Boltzmann finite-element method provides the novel ability to simulate hundreds of realistic and deformable red blood cells and produce continuum-scale physics at physiologic hematocrit and low arterial-shear rates. The new method is developed and shown to produce single red blood cell deformation consistent with experimental results in flow chambers. Simulations of 77 to 216 cells in unbounded shear flow produce bulk and micro-rheological behavior consistent with experimental results in viscometers and tubes, including shear-thinning behavior at various shear rates. Investigation of the local stress environment in blood indicates that, although the majority of platelets experience a time-averaged shear stress equal to the suspension stress, 25% of platelets experience a localized shear stress greater than twice the suspension stress. The lattice-Boltzmann finite-element method developed in this work has been shown capable of investigating the fundamental gap between cell-level processes and continuum-level function. The complex stress environment in whole blood has been described for simple shear flow and the methodology may be extended to more complex flow geometries and incorporate platelet-adhesion models for adhesion studies. Thus, this research fits into the greater objective of prediction and control of platelet deposition in clinical and engineering applications. Furthermore, the ability to bridge the gap between cell-level processes and continuum-level function is useful in other important cardiovascular areas including leukocyte adhesion, platelet aggregate embolization, and artheriogenesis.