Recently we have extended our codes based on the Schwinger variational iterative method in order to study elastic electron scattering by non-planar molecules with symmetries reducible to the C2v point group and also to include a correlation- polarization contribution to the electron-molecule interaction potential. In this work we report the first application of these newly extended codes to the calculation of cross sections for low-energy elastic scattering of electron by methane. Differential, integral and momentum-transfer cross sections were calculated in the 0.1-50 eV incident energy range. Comparison of our results with the extensive available data, both experimental and theoretical, reveals the reliability of our method. Particularly, the Ramsauer minimum at around 0.4 eV and the resonance structure at around 8 eV are well reproduced in our calculations.