Tire failures, such as tread separation and sidewall zipper fracture, occur when internal flaws (cracks) nucleate and grow to a critical size as result of fatigue or cyclic loading. Sudden and catastrophic rupture takes place at this critical crack size because the strain energy release rate exceeds the tear energy of the rubber in the tire. The above-mentioned tire failures can lead to loss of vehicle stability and control, and it is important to develop predictive models and computational tools that address this problem. The objective of this article was to develop a cohesive zone model for rubber to numerically predict crack growth in a rubber component under dynamic tearing. The cohesive zone model for rubber was embedded into the material constitutive equation via a user-defined material subroutine (VUMAT) of ABAQUS. It consisted of three parts: (1) hyperviscoelastic behavior before damage, (2) damage initiation based on the critical strain energy density, and (3) hyperviscoelastic behavior after damage initiation. Crack growth in the tensile strip and pure shear specimens was simulated in ABAQUS Explicit, and good agreement was reported between finite element analysis predictions and test results.