Cerebral blood volume (CBV) changes significantly with brain activation, whether measured using positron emission tomography, functional magnetic resonance imaging (fMRI), or optical microscopy. If cerebral vessels are considered to be impermeable, the contents of the skull incompressible, and the skull itself inextensible, task- and hypercapnia-related changes of CBV could produce intolerable changes of intracranial pressure. Because it is becoming clear that CBV may be useful as a well-localized marker of neural activity changes, a resolution of this apparent paradox is needed. We have explored the idea that much of the change in CBV is facilitated by exchange of water between capillaries and surrounding tissue. To this end, we developed a novel hemodynamic boundary-value model and found approximate solutions using a numerical algorithm. We also constructed a macroscopic experimental model of a single capillary to provide biophysical insight. Both experiment and theory model capillary membranes as elastic and permeable. For a realistic change of input pressure, a relative pipe volume change of 21±5% was observed when using the experimental setup, compared with the value of approximately 17±1% when this quantity was calculated from the mathematical model. Volume, axial flow, and pressure changes are in the expected range.