Capsules are liquid droplets enclosed by a thin membrane which can resist shear deformation. They are widely found in nature (e.g. red blood cells) and in numerous applications (e.g. food, cosmetic, biomedical and pharmaceutical industries [1]), where they often flow through a complicated network of tubes or channels: this is the case for RBCs in the human circulation or for artificial capsules flowing through microfluidic devices. Central to these flows is the dynamic motion of capsules at bifurcations, in particular the question of path selection. A good understanding of this problem is indeed needed to elucidate some intriguing phenomena in human circulation and to design multi-branched microfluidic devices to sort or enrich suspensions of artificial microcapsules or biological cells depending on their properties. Thanks to the extensive in vivo and in vitro experiments conducted on blood flows in branched capillaries or microchannels [2], it has been well established that the daughter branch with a higher flow rate receives a larger number of RBCs than the other branch: this is classically referred to as the Zweifach-Fung effect [3,4]. Similar phenomena have also been observed in experiments on suspensions, where the RBCs are modelled as flexible disks and the white blood cells as solid spheres [5], and in dilute suspensions of solid spheres [6]. This is a consequence of the plasma skimming effect due to the particlefree layer near the wall of the vessel [7] and of the particle screening effect due to the deviation of the particle trajectories from the background flow fluid streamlines as a result of the hydrodynamic interaction between the particles and vessel geometry at the bifurcation [8, 6]. In the dilute limit, the problem has, however, not been thoroughly studied experimentally, possibly due to the difficulty of manipulating individual cells. The problem has mostly been studied in recent years using two-dimensional numerical models [9, 10]. The results showed that, at equal flow rate between the two downstream channels, the capsule tends to flow into the side branch in particular when the capsule is highly deformable. But to what extent the results obtained from previous two-dimensional simulations can be applied to three-dimensional flows remains unclear. The objective of the present study is to conduct a systematic and in-depth three-dimensional numerical study of a deformable capsule in a branched tube and to determine the influence of inertia. Contrary to many biological systems, for which neglecting inertia is a good assumption, capsules are not necessarily small in size and the flow speed can be fast in some applications [11].