One of the main bottlenecks in air transport operations is the runway capacity at airports. As such, managing aircraft arrivals and departures is of great importance to ensure smooth and efficient airport operations. The research objective of this article is to model the airport departure process at Vienna Airport under the influence of uncertainty. In order to simulate the departure process, the process is divided into smaller pieces. The process consists of push-back, unimpeded taxi-out time, additional taxi-out time, waiting time and runway occupancy time. The waiting time is found by using queue theory and analysing runway availability. The other phases are modelled as stochastic variables, given by an appropriate distribution obtained from historical data. The model is able to simulate runways with segregated (departures only) and mixed-mode operations. A Monte Carlo simulation is used to estimate the flight departure duration.