Maintaining the ionic and chemical composition of the extracellular spaces in the brain is extremely important for its health and function. However, the brain lacks a conventional lymphatic system to remove metabolic waste. It has been proposed that the fluid movement through the paravascular space (PVS) surrounding penetrating arteries can help remove metabolites from the brain. The dynamics of fluid movement in the PVS and its interaction with arterial dilation and brain mechanics are not well understood. Here, we performed simulations to understand how arterial pulsations and dilations interact with brain deformability to drive fluid flow in the PVS. In simulations with compliant brain tissue, arterial pulsations did not drive appreciable flows in the PVS. In contrast, when the artery dilated with dynamics like those seen during functional hyperemia, there was a marked movement of fluid through the PVS. Our simulations suggest that in addition to its other purposes, functional hyperemia may serve to increase fluid exchange between the PVS and the subarachnoid space, improving the clearance of metabolic waste. We measured displacement of the blood vessels and the brain tissue simultaneously in awake, headfixed mice using two-photon microscopy. Our measurements show that brain tissue can deform in response to fluid movement in the PVS, as predicted by simulations. The results from our simulations and experiments show that the deformability of the soft brain tissue needs to be accounted for when studying fluid flow and metabolite transport in the brain.