Traumatic brain injuries (TBI) affect millions of people each year. While research has been dedicated to determining the mechanical properties of the uninjured brain, there has been a lack of investigation on the mechanical properties of the brain after experiencing a primary blast-induced TBI. In this paper, whole porcine brains were exposed to a shock wave to simulate blast-induced TBI. First, ten (10) brains were subjected to unconfined compression experiments immediately following shock wave exposure. In addition, 22 brains exposed to a shock wave were placed in saline solution and refrigerated between 30 minutes and 6.0 hours before undergoing unconfined compression experiments. This study aimed to investigate the effect of a time delay on the viscoelastic properties in the event that an experiment cannot be completed immediately. Samples from both soaked and freshly extracted brains were subjected to compressive rates of 5, 50, and 500 mm/min during the unconfined compression experiments. The fractional Zener (FZ) viscoelastic model was applied to obtain the brain's material properties. The length of time in the solution statistically influenced three of the four FZ coefficients, E0 (instantaneous elastic response), τ0 (relaxation time), and α (fractional order). Further, the compressive rate statistically influenced τ0 and α.