The low strain-rate response of brain parenchyma is critical to predicting prognosis in cases of hydrocephalus or cerebral edema, including in the prediction of brain stem herniation. Although rate-dependent responses of brain parenchyma are well known to arise from both viscoelasticity at higher strain rates, and it is not clear whether the tissue behaves as a fluid or a solid when loaded over periods of hours to days, and the extrapolation of rate sensitivity to lower strain rates is not clear. To address this, unconfined compression-isometric hold tests were performed on samples of white matter from porcine brains at strain rates ranging from 2/s to 2 × 10−6/s. Results showed that the apparent Young's modulus dropped from ∼3000 Pa to ∼160 Pa over this range following a power law, and that an equilibrium Young's modulus of ∼100 Pa was reached. Results reveal that brain parenchyma behaves as a compliant solid at low strain rates, and suggest that brain stem herniation is resisted by an elastic energy barrier.