2D cellular reflection processes of detonation waves on different angle wedges were investigated by using a fifth-order weighted essentially non-oscillatory (WENO) scheme with Additive Runge Kutta(ARK) time step method. A detailed chemical kinetics model was adopted to construct the mass fraction of species in a stoichiometric H-2-O-2 mixture diluted by Argon. It was found that a Mach reflection as well as a regular reflection existed over the wedge. The regular cellular detonation wave was disturbed where the Mach reflection occurs, which made the cells become smaller and the shape get distorted. It was shown from the numerical results that when the angle is less than 30, the trajectory of the triple points was not linearly distributed. However, it got close to be a linear distribution with the increase of the angle. With the increase of wedge angle, the pressure on the wedge surface got increased especially for the apex which suffered a higher pressure. The state of the chemical reaction was indicated by the intermediate concentration in which the incident shock was weaker than the Mach stem. These numerical results and conclusions were significant for the evaluation of detonation threats and meaningful in engineering application. Copyright (C) 2015, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.