Three-dimensional structures of detonation wave propagating in tubes were investigated. Inviscid fluid dynamics equations coupled with a conservation equation of reaction progress variable were analyzed by a MUSCL-type TVD scheme and four stage Runge-Kutta time integration. Variable-v formulation was used to account for the variable properties between unburned and burned states and the chemical reaction was modeled by using a simplified one-step irreversible kinetics model. The computational code was parallelized based on domain decomposition technique using MPI-II message passing library. The computations were carried out using an in-house Windows cluster system with AMD AthlonTM XP and AthlonTM 64-X2 processor cores. The computational domain consisted of through a square-shaped duct with wall conditions on its lateral boundaries. As an initial condition, analytical ZND solution was distributed over the computational domain with small disturbances. The unsteady computational results in three-dimension show the detailed mechanisms of rectangular and diagonal mode of detonation wave instabilities resulting same cell length but different cell width in smoked-foil record.