Filtration combustion involves exothermic reactions within a porous matrix. The combustion of gaseous fuel and oxidizer filtrating through an inert matrix is one example of filtration combustion. Low velocity filtration combustion, in which the speed of the reaction front is less than 1 mm/s, differs substantially from homogeneous premixed combustion. In this paper, we investigate the low-velocity filtration combustion reaction of lean methane/air mixtures flowing through a packed bed and compare to experimental results. Our one-dimensional model includes gas-phase transport, radiation, interphase heat exchange, and solid conduction. Reaction is represented with a complete methane/air kinetics mechanism. Our results for solid temperature agree well with experiments for a mixture with an equivalence ratio of 0.15. Consistent with the existing theory on filtration combustion, we determined that gas-phase transport is not important to wave propagation at this condition. Gas-phase dispersion is important only at higher equivalence ratios. Over a wide range of equivalence ratios, the computed wave speeds show the same trends as the theoretical predictions but are generally higher.