Hypothermic machine perfusion (HMP) is regarded as a better preservation method for donor livers than cold storage. During HMP, livers are perfused through the inlet blood vessels, namely the hepatic artery (HA) and the portal vein (PV). In previous HMP feasibility studies of porcine and human livers, we observed that the PV flow decreased while the HA flow increased. This flow competition restored either spontaneously or by lowering the HA pressure (P_HA). Since this phenomenon had never been observed before and because it affects the HMP stability, it is essential to gain more insight into the determinants of flow competition. To this end, we investigated the influence of the HMP boundary conditions on liver flows during controlled experiments. This paper presents the flow effects induced by increasing P_HA and by obstructing the outlet blood vessel, which is the vena cava inferior (VCI). Flow competition was evoked by increasing P_HA to 55–70 mmHg, as well as by obstructing the VCI. Remarkably, a severe obstruction resulted in a repetitive and alternating tradeoff between the HA and PV flows. These phenomena could be related to intra-sinusoidal pressure alterations. Consequently, a higher P_HA is most likely transmitted to the sinusoidal level. This increased sinusoidal pressure reduces the pressure drop between the PV and the sinusoids, leading to a decreased PV perfusion. Flow competition has not been encountered or evoked under physiological conditions and should be taken into account for the design of liver HMP protocols. Nevertheless, more research is necessary to determine the optimal parameters for stable HMP.