We have studied the muon neutrino and antineutrino quasi-elastic (QEL) scattering reactions (ν μ n → μ − p andν μ p → μ + 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 ν μ (ν μ ) charged-current cross section. The results for the flux-averaged QEL cross sections in the (anti)neutrino energy interval 3-100 GeV are σ qel ν μ = (0.92 ± 0.02(stat) ± 0.06(syst)) × 10 −38 cm 2 and σ qel ν μ = (0.81 ± 0.05(stat) ± 0.09(syst)) × 10 −38 cm 2 for neutrino and antineutrino, respectively. The axial mass parameter M A was extracted from the measured quasi-elastic neutrino cross section. The corresponding result is M A = 1.05±0.02(stat)±0.06(syst) GeV. It is consistent with the axial mass values recalculated from the antineutrino cross section and extracted from the pure Q 2 shape analysis of the high purity sample of ν μ quasielastic 2-track events, but has smaller systematic error and should be quoted as the main result of this work. Our measured M A 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 A is lower than those recently published by K2K and MiniBooNE Collaborations. However, within the large errors quoted by these experiments on M A , these results are compatible with the more precise NOMAD value.PACS 13.15.+g · 25.30.Pt