The mechanics of platelet initial adhesion due to interactions between GPIb receptor with von Willebrand factor (vWf) multimers is essential for thrombus growth and the regulation of this process. Multimeric structure of vWf is known to make adhesion sensitive to the hydrodynamic conditions, providing intensive platelet aggregation in bulk fluid for high shear rates. But it is still unclear how it affects the dynamics of platelet motion near vessel walls and efficiency of their adhesion to surfaces. Our goal is to resolve the principal issues in the mechanics of platelet initial attachment via GPIb-vWf bonds in near-wall flow conditions: when the platelet tends to roll or slide and how this dynamics depends on the size, conformation and adhesive properties of the vWf multimers. We employ a 3D computer model based on a combination of the Lattice Boltzmann method with mesoscopic particle dynamics for explicit simulation of vWf-mediated blood platelet adhesion in shear flow. Our results reveal the link between the mechanics of platelet initial adhesion and the physico-chemical properties of vWf multimers. This has implications in further theoretical investigation of thrombus growth dynamics, as well as the interpretation of in vitro experimental data. © EDP Sciences, 2018.