Absolute measurements of differential electron-collision cross sections have been performed for the vibrational excitation of methane in its electronic ground state at impact energies of 15 eV and, for the first time, at 30 eV, in the 8 degrees-95 degrees angular range. The normalization to the absolute scale has been carried out using the inelastic/elastic ratios and the absolute elastic differential cross section obtained from a relative flow technique recently developed in our laboratory, in which the elastic differential cross section of methane was compared to that of nitrogen at each impact energy and at each scattering angle. Special attention has been given to the small scattering angular range (less than or equal to 40 degrees) where minima have been observed in the vibrational cross sections and where simultaneous independent measurements have been made on two different electron spectrometers.