Homing of circulating tumour cells (CTC) at distant sites represents a critical event in metastasis dissemination. In addition to physical entrapment, probably responsible of the majority of the homing events, the vascular system provides with geometrical factors that govern the flow biomechanics and impact on the fate of the CTC. Here we mathematically explored the distribution of velocities and the corresponding streamlines at the bifurcations of large blood vessel and characterized an area of low-velocity at the carina of bifurcation that favours the residence of CTC. In addition to this fluid physics effect, the adhesive capabilities of the CTC provide with a biological competitive advantage resulting in a marginal but systematic arrest as evidenced by dynamic in vitro recirculation in Y-microchannels and by perfusion in in vivo mice models. Our results also demonstrate that viscosity, as a main determinant of the Reynolds number that define flow biomechanics, may be modulated to limit or impair CTC accumulation at the bifurcation of blood vessels, in agreement with the apparent positive effect observed in the clinical setting by anticoagulants in advanced oncology disease.