  The profile of the longitudinal development of showers produced by ultra-high
energy cosmic rays carries information related to the interaction properties of
the primary particles with atmospheric nuclei. In this work, we present the
first measurement of the average shower profile in traversed atmospheric depth
at the Pierre Auger Observatory. The shapes of profiles are well reproduced by
the Gaisser-Hillas parametrization within the range studied, for E > 10^{17.8}
eV. A detailed analysis of the systematic uncertainties is performed using 10
years of data and a full detector simulation. The average shape is quantified
using two variables related to the width and asymmetry of the profile, and the
results are compared with predictions of hadronic interaction models for
different primary particles.
