The specific adhesive interaction between a non-spherical particle and a cell layer under a linear shear flow is analyzed. The effect of the characteristic particle size, expressed in terms of the volume V, and shape, expressed in terms of the aspect ratio gamma, on the adhesive strength is investigated. It is shown that for a fixed shape, there exists an optimal volume V(opt) for which the adhesive strength has a maximum. A surprisingly accurate relationship has been derived between the optimal volume V(opt) and the ratio microS/m(r) (wall shear stress to the receptors surface density) having the form V(opt)=alpha(m(r)/microS)(beta). Also, oblate particles have been shown to adhere more effectively to the biological substrate than classical spherical particles for the same volume V. As a consequence, non-spherical particles can carry a larger amount of drugs and contrast agents than classical spherical particles with the same adhesive strength, improving the therapeutic and imaging efficacy. The formulae and the procedures described in the present work can guide the optimal design of intravascularly injectable micro/nano carriers.