Rock avalanches typically entail the flow-like motion of angular rock blocks and fragments of diverse size. Numerical simulations are instrumental in understanding their dynamic process, supporting hazard and risk assessments. Simplified failure criteria, such as the Mohr-Coulomb or Drucker-Prager, are commonly adopted in landslide models relying on the material point method (MPM). However, these criteria cannot capture the transitions between solid-like, liquid-like, and gas-like behaviors exhibited by granular materials. Here, we relied on the moving least-squares MPM, which offers high computing efficiency and stability, and adopted a nonlocal mu(I) rheology model implemented by Haeri and Skonieczny (Comput Methods Appl Mech Eng, 2022). This approach can account for the rate-dependent, pressure-dependent, and size-dependent characteristics of friction in granular materials. By simulating a small-scale flume experiment as well as a large-scale event (the Nayong rock avalanche in Guizhou, China), we verified that the nonlocal mu(I) rheology model can capture the motion and deposition processes in rock avalanches effectively. This feature can be advantageous in physically based hazard assessments of such events.