Understanding the brain’s response to multiple loadings requires knowledge of how straining changes the mechanical response of brain tissue. We studied the inelastic behavior of bovine white matter and found that when this tissue is stretched beyond a critical strain threshold, its reloading stiffness drops. An upper bound for this strain threshold was characterized, and was found to be strain rate dependent at low strain rates and strain rate independent at higher strain rates. Results suggest that permanent changes to tissue mechanics can occur at strains below those believed to cause physiological disruption or rupture of axons. Such behavior is characteristic of disentanglement in fibrous-networked solids, in which strain-induced mechanical changes may result from fiber realignment rather than fiber breakage.