In the present theoretical study, we investigated the formation of CHx (x = 0-4) on corrugated Ru(100)B and Ru(111) surfaces. Our results demonstrate that on Ru(100)B and Ru(111) surfaces, C and CH intermediates are the most stable adsorbed CHx species respectively. This indicates that the distribution of the CHx adsorbed species will depend on the surface structure. The results obtained from the kinetic analysis show that the formation of CH4 on Ru(100)B surface is slower than that on the Ru(111) surface. Furthermore, the activation of CH4 is easier on the Ru(111) surface than on the Ru(100)B surface.