Abstract. We have studied the muon neutrino and antineutrino quasi-elastic (QEL) scattering reactions {vnn -^ jjTp and VnP -^ n'n) using a set of experimental data collected by the NOMAD collaboration. We have performed measurements of the cross-section of these processes on a nuclear target (mainly Carbon) normalizing it to the total Vn {vn) charged current cross-section. The results for the flux averaged QEL cross-sections in the (anti)neutrino energy interval 3 -100 GeV are {<^qel)ui, = (0.92±0.02(siai)±0.06(sj/si)) x 10"^® cm^ and {aqei)i?i, = (0.81±0.05(siai)±0.09(sj/si)) x 10"^® cm^ for neutrino and antineutrino, respectively. The axial mass parameter M^ was extracted from the measured quasi-elastic neutrino cross-section. The corresponding result is M^ = 1.05 ± 0.02(siai) ± 0.06(sj/si) GeV. It is consistent with the axial mass values recalculated from the antineutrino cross-section and extracted from the pure Q shape analysis of the high purity sample of f^i quasi-elastic 2-track events, but has smaller systematic error and should be quoted as the main result of this work. Our measured M^ is found to be in good agreement with the world average value obtained in previous deuterium filled bubble chamber experiments. The NOMAD measurement of M^ is lower than those recently published by K2K and MiniBooNE collaborations. However, within the large errors quoted by these experiments on M^, these results are compatible with the more precise NOMAD value.