The aim of this study is investigated about the three dimensional structure of gaseous detonation wave propagation. The analysis was carried out by the three-dimensional invisicid fluid dynamics equation coupled with a conservation equation of reaction progress variable with variable-γ formulation and one-step irreversible reaction. The inviscid fluid dynamics equations are solved by a MUSCL-type TVD scheme and 4th order accurate Runge-Kutta time integration scheme and the CFD codes are parallelized based on domain decomposition technique using MPI library. First, the Champan-Jouguet (C-J) and steady Zel’dovich-von Neumann- Doring(ZND) structure analysis solutions were carried out. These results are used as initial condition for two- and three-dimensional numerical simulations. Second, the study is carried out about two-dimensional problems. In the two-dimensional simulations, a series of numerical studies are carried out for the different regimes of the detonation phenomena to investigate the computational requirements for the simulation of the detonation wave cell structure by varying the reaction constants and grid resolutions. The computational results are investigated by comparing the solution of steady ZND structure to draw out the minimum grid resolutions and the size of the computational domain for the capturing cell structures of the different regimes of the detonation phenomena. Next, three dimensional structure of detonation wave propagating in a square and circular tube was investigated. In a square tube, three-dimensional unsteady analysis results in the smoked-foil records caused by the instabilities of the detonation waves, which showed the rectangular and diagonal modes of detonation instability depending on the initial conditions of disturbances and the spinning detonation for case of small reaction constant. And last, in a circular tube, a series of parametric study was carried out to investigate the different modes of cell structure formation by changing pre-exponential factor. Maximum pressure trace was recorded along the tube wall to investigate the detonation cell structures. The unsteady results obtained in three dimensions revealed the generation mechanism of the wave front structure of two-, three- and four-cell mode detonations. A six-cell mode detonation could be obtained using a finer grid. It was found that the detonation cell number increased, but the cell width and length decreased with the increase in pre-exponential factor. In all the multi-cell modes, the detonation wave structures and smoked-foil records on the wall are formed by the propagation of transverse waves along the wall in clockwise and counter-clockwise while the slapping move in radial direction. Comparison with two-dimensional simulation confirms the effect of the slapping transverse wave in radial direction. As a result, the detonation wave front structures changes from polygonal shape to windmill shape with multiple fans, periodically.