We report reduced dimensionality quantum mechanical calculations of the rate constants of the Mu + CH4 -> MuH + CH3 reaction. An ab initio potential energy surface is developed to describe the reactive process in a two-dimensional space and incorporates the zero-point energy of the spectator modes using the CCSD(T, full)/cc-pVTZ//MP2(full)/cc-pVTZ method. Scattering calculations produced reaction probabilities and total rate constants. MuH products are formed mainly in their ground vibrational state. Reaction from the first stretch excited state of CH4(s = 1) is found to be more important than that from CH4(s = 0) ground state. Rate constants exhibit pronounced quantum tunneling in the considered temperature range [200-2000 K] and a reasonable comparison is noticed with experiment. (c) 2005 Elsevier B.V. All rights reserved.