Systemically administered ligand-coated nanoparticles have been proved to recognize biological targets in-vivo. This can provide breakthrough solutions for the early detection, imaging and cure of diseases. In cardiovascular applications, nanoparticles have been targeted directly to the diseased vasculature, and such delivery approach is becoming increasingly popular even in cancer research, supported by the growing body of evidences on the biological differences between normal and tumor vasculature. This work focuses on the optimal design of nanoparticles for vascular targeting throughout mathematical modeling. Such nanoparticles should be engineered so as to recognize specifically and adhere firmly to the diseased vessel walls withstanding the hydrodynamic dislodging forces and control uptake by the endothelial cells. A stochastic approach for predicting the adhesion strength of nanoparticles to a cell layer under flow has been coupled to a mathematical model for the receptor-mediated endocytosis of nanoparticles. The main geometrical, biophysical and biological parameters governing both events have been identified and their relative importance highlighted. Three different states for the particle/cell system have been predicted, namely no adhesion, adhesion with no endocytosis and adhesion with endocytosis, based upon the geometrical and biophysical properties of the particle and the biological conditions at the site of adhesion. Design maps have been generated to be used as a preliminary reference for choosing the properties of the nanoparticle as a function of physiological parameters, as the wall shear stress and the receptors surface density, at the site of desired adhesion within the target vasculature.