•The effective muon attenuation and absorption lengths of air showers are investigated.•Air shower data of the KASCADE-Grande observatory is analyzed.•Predictions of the models SIBYLL 2.1, EPOS-LHC, QGSJET-II-02 and -04 are tested.•The studied models fail to describe consistently the attenuation of the muon data. The evolution of the muon content of very high energy air showers (EAS) in the atmosphere is investigated with data of the KASCADE-Grande observatory. For this purpose, the muon attenuation length in the atmosphere is obtained to Λμ=1256±85−232+229(syst)g/cm2 from the experimental data for shower energies between 1016.3 and 1017.0 eV. Comparison of this quantity with predictions of the high-energy hadronic interaction models QGSJET-II-02, SIBYLL 2.1, QGSJET-II-04 and EPOS-LHC reveals that the attenuation of the muon content of measured EAS in the atmosphere is lower than predicted. Deviations are, however, less significant with the post-LHC models. The presence of such deviations seems to be related to a difference between the simulated and the measured zenith angle evolutions of the lateral muon density distributions of EAS, which also causes a discrepancy between the measured absorption lengths of the density of shower muons and the predicted ones at large distances from the EAS core. The studied deficiencies show that all four considered hadronic interaction models fail to describe consistently the zenith angle evolution of the muon content of EAS in the aforesaid energy regime.