Nanoparticles have a wide range of applications in fluid systems. In the present paper, cavitation of water with SiO₂ and polyethylene nanoparticles are investigated by molecular dynamics simulations. The effects of particle type and size are discussed by computing the nucleation rates and free energy of critical bubble in water via the Voronoi tessellation and the Mean First Passage Time method. The variation of hydrogen bond network is also analyzed. Results show that the nucleation rates of water with both nanoparticles are one order of magnitude larger than the value of pure water. At the same condition, nucleation rate of water with polyethylene nanoparticle is about 2.2 times larger than the value of water with SiO₂ nanoparticle. For different particle sizes, the effect of particle size on the nucleation rates and free energy of critical bubble can be neglected when particle radius is smaller than half of the critical bubble radius. It reaches the value of planar surface when particle radius is 10 times larger than the critical bubble radius. Current study also shows that both SiO₂ and polyethylene nanoparticles promote the cavitation of water. The most possible cause of the promotion is the decrease of average number and average energy of the formed hydrogen bonds.