The origin of ultra-high energy cosmic rays is unknown and the mass composition is one of the key observables to understand the origin. The mass composition is estimated by comparing a prediction of the depth of maximum of shower developments, $X_{max}$, with experimental data, however, the $X_{max}$ prediction depends on the choice of hadronic interaction modes in the simulation. One of the proposed sources of the difference is the different modeling of diffractive collisions among the models. In this work, we estimate the effect of detail of diffractive collisions at the first interaction of cosmic-rays with atmospheric nuclei on the air shower developments by using the air shower simulation package COSMOS 8.035. The results show that the modeling of diffractive collisions at the first interaction is not the main source of the model discrepancies of the $X_{max}$ prediction.