Current models of the formation of the first stars in the universe suggest that these stars were very massive, having a typical mass scale of hundreds of solar masses. Many of them would die as pair instability supernovae (PSNe) which might be the biggest explosions of the universe. Most theoretical models for the PSNe are based on one-dimensional simulations; until now, multidimensional simulations have been scarce because of their complexity. However, multidimensional simulations are essential because, when the star dies in a supernova, the assumption of spherical symmetry of the star breaks down on a large scale due to fluid instabilities generated during the explosion. These instabilities are fundamentally multidimensional. We present the results from multidimensional numerical studies of PSNe with a new radiation-hydrodynamics code, CASTRO and with realistic nuclear reaction networks. We simulate the fluid instabilities that occur in multiple spatial dimensions and discuss how the resulting mixing affects the explosion, mixing, and nucleosynthesis of these supernovae. Our simulations can provide useful predictions for the observational signatures of PSNe. They might soon be examined by the forthcoming telescopes such as the James Webb Space Telescope.