The ongoing conflict against terrorism has resulted in an escalation of blast-induced traumatic brain injuries (bTBI) caused by improvised explosive devices (IEDs). The destructive IEDs create a blast wave that travels through the atmosphere. Blast-induced traumatic brain injuries, attributed to the blast wave, can cause life-threatening injuries and fatalities. This study aims to find a surrogate brain material for assessing the effectiveness of head protection systems designed to mitigate bTBI. Polydimethylsiloxane (PDMS) is considered as the surrogate brain material. The stiffness of PDMS (Sylgard 184, Dow Corning Corp.) can be controlled by varying the ratio of base and curing agent. Cylindrical PDMS specimen with ratios of 1:10, 1:70, and 1:80 were subjected to unconfined compression experiments at linear rates of 5 mm/min, 50 mm/min, and 500 mm/min. A ramp-hold strain profile was used to simulate a stress relaxation experiment. The fractional Zener viscoelastic model was used to describe the stress relaxation response, after optimization of the material constants for the brain surrogate and shock wave exposure brain tissue. The results show that the low cost PDMS can be used as a surrogate brain material to study the dynamic brain response to blast wave exposure.