In this work we present a theoretical study on electrons scattering by CH4 in the intermediate energy range. More specifically, we report integral and differential cross sections for electron scattering by CH4 in the (10 ~ 300) eV range by the Schwinger multichannel method using plane waves as a trial basis set (SMC-PW). To include exchange effects we have used the Born-Ochkur model. Our aim is to study the numerical stability of the cross sections and our calculated results compared with experimental data and theoretical studies are encouraging.