Based on periodic Density Functional Theory (DFT) calculations, carried out using a standard generalized gradient approximation type exchange-correlation functional including or not van der Waals dispersive forces, the ability of the cubic delta-MoC(001) surface to capture methane at room temperature is suggested. Adsorption on the orthorhombic beta-Mo2C(001) surfaces, with two possible terminations, has been also considered and, in each case, several molecular orientations have been tested with one, two, or three hydrogen atoms pointing towards the surface on all high-symmetry adsorption sites. The DFT results indicate that the delta-MoC(001) surface shows a better affinity towards CH4 than beta-Mo2C(001). The calculated adsorption energy values on delta-MoC(001) surfaces are larger, and hence better, than on other methane capturing materials such as metal organic frameworks. Besides, the theoretical desorption temperature values estimated from the Redhead equation indicate that methane would desorb at 330 K when adsorbed on the delta-MoC(001) surface, whereas this temperature is lower than 150 K when the adsorption involves beta-Mo2C(001). Despite this, adsorbed methane presents a very similar structure compared to the isolated molecule, due to a weak molecular interaction between the adsorbate and the surface. Therefore, the activation of methane molecules is not observed, so these surfaces are, in principle, not recommended as possible methane dry reforming catalysts.