Methane is a promising propellant for liquid rocket engines. As a regenerative coolant, it would be close to its critical point, complicating cooling analysis. This study encompasses the development and validation of a new, open-source computational fluid dynamics (CFD) method for analysis of methane cooling channels. Validation with experimental data has been carried out, showing an accuracy within 20 K for wall temperature and 10% for pressure drop. It is shown that the turbulence model has only a limited impact on the simulation results and that the wall function approach generates valid results. Finally, a cooling analysis is performed to compare two thrust chamber materials. A traditional copper alloy is compared to aluminium as chamber material for a small moderate-pressure oxygen/ methane engine. The analyses show that aluminium is a feasible chamber material only if a thermal barrier coating is applied. In addition, a significantly higher cooling channel pressure drop is incurred for an aluminium chamber than for a copper chamber due to the lower allowable temperature.