  Cosmic ray data may allow the determination of the proton-air cross section
at ultra-high energy. For example, the distribution of the first interaction
point in air showers reflects the particle production cross section. As it is
not possible to observe the point of the first interaction $X_{\rm 1}$ of a
cosmic ray primary particle directly, other air shower observables must be
linked to $X_{\rm 1}$. This introduces an inherent dependence of the derived
cross section on the general understanding and modeling of air showers and,
therfore, on the hadronic interaction model used for the Monte Carlo
simulation. We quantify the uncertainties arising from the model dependence by
varying some characteristic features of high-energy hadron production.
