Molecular dynamics (MD) simulations have been used to study the diffusion of methane as a small molecule penetrant example in cis-1,4-polybutadiene (PBD). The non-bonded potential for an ’anisotropic’ united atom (AUA) representation of the -CH=group was calibrated by adjusting the constants to fit experimental volume temperature data for the polymer melt. This potential was used along with an already available AUA function for the -CH2-group. The diffusion coefficient of methane was determined via MD simulation over a wide range of temperature. The results agree well with near room temperature experimental values for N2 in cis-PBD. The latter gas is similar in diffusion behaviour to methane. The mechanism of diffusion in terms of the nature of the diffusive jump process and its response to temperature is found to be similar to that in atactic polypropylene and polyethylene melts. At low temperatures the penetrant is trapped for relatively long periods in a cage of surrounding polymer and makes occasional large jumps. As temperature increases the size of the jumps increases further. The quiescent trapped periods disappear and a liquid-like scattering regime prevails. This change in mechanism as temperature increases is accompanied by a decrease in activation energy. The diffusion in PBD is faster than in other hydrocarbon polymers studied so far by simulation (polyethylene, polyisobutylene and atactic polypropylene). The order of diffusion coefficients correlates with the free volumes available in the polymer hosts.