Dynamic cracks in rubber can spontaneously oscillate under certain biaxial strain conditions [R. D. Deegan et al., Phys. Rev. Lett. 88, 014304 (2002)]. We have found that this unusual phenomenon can be understood from the unique mechanical properties of rubber: hyperelasticity, viscoelasticity, and nonlocal elasticity. While all these are important, the decisive role of nonlocality needs to be particularly emphasized. Through numerical simulations with a lattice model, we have quantitatively reproduced the experimental results.