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The model dependence of the development of extensive air showers generated byhigh-energy cosmic-ray particles in the atmosphere is studied. The increase ofproton-proton and proton-air inelastic cross-sections and values for theelasticity are varied in the hadronic interaction model QGSJET. Using theCORSIKA simulation program, the impact of these changes is investigated on airshower observables like the average depth of the shower maximum X_max and thenumber of muons and electrons at ground level. Calculating the mean logarithmicmass from experimental X_max values, it is found that a moderate logarithmicincrease of the proton-proton inelastic cross-section from sigma_pp^inel=51 mbat E_0=10^6 GeV to sigma_pp^inel=64 mb at E_0=10^8 GeV and an elasticity,additionally increased by 10% to 15%, describes the data best. Using theseparameters, the mean logarithmic mass lna derived from X_max measurements iscompatible with the extrapolations of the results of direct measurements tohigh energies using the poly-gonato model

On total inelastic cross sections and the average depth of the maximum of extensive air showers