Inflammation is a key physiological process, important in infections, autoimmune diseases, and chronic diseases. During inflammation, circulating neutrophils roll on, and eventually tether to, the endothelial lining of blood vessels, allowing them to exit the bloodstream and enter the surrounding tissue. This process is mediated by the selectin family of adhesion molecules. A three-dimensional computational model was applied to neutrophils with pseudopods to study the effect of cell shape on the hydrodynamic transport of neutrophils. It was found that neutrophils experience more frequent collisions compared to prolate spheroids of equal volume and length. Longer pseudopods and lower shear rates increase the collision time integral contact area, a predictor of binding potential. The contact between the neutrophil and the vessel wall was found to be focused predominantly on the pseudopod tip. Multiscale Adhesive Dynamics was used to simulate the behavior of pseudopod-containing neutrophils mediated by P-selectin/PSGL-1 binding kinetics. In contrast to the hydrodynamic model, P-selectin/PSGL-1 binding slows the neutrophil's translation in the direction of flow and causes the neutrophil to swing around perpendicular to flow. Several behaviors observed during the simulations, including tethering and firm adhesion upon contact with the endothelium, were qualitatively consistent with in vivo data of murine neutrophils with pseudopods. Increasing shear rate, receptor count, and bond formation rate increased the incidence of firm adhesion. Tethering was conserved across a range of physiological shear rates and was insensitive in the number of surface PSGL-1 molecules. E-selectin is upregulated on stimulated endothelial cells and binds to sLex, a common constituent on selectin ligands. Molecular simulations were used to compare the dissociation mechanisms of sLex with mouse and human E-selectin, which differ by 29 amino acids in the region of interest. Mouse E-selectin in complex with sLex was found to take longer to dissociate, which was corroborated with rolling experiments. Modeling of selectin-mediated neutrophil interaction with the endothelium allows for a more detailed understanding of the free-flow capture and rolling mechanisms that propel the inflammation cascade. Clinically, engineering selectins for greater adhesion could lead to improved selectin-based leukocyte or circulating tumor cell isolation of patient blood.