In recent decades, the exposure of aviation crews and passengers to cosmic radiation has been progressively increasing due to the growing need of flights. Therefore, there is a need for radiation assessment software tools to act as a complement to other radiation protection techniques and countermeasures. In this work, the exposure to cosmic radiation is estimated for flights from Athens International Airport to various international destinations, by performing Monte Carlo simulations with the validated tool DYASTIMA/DYASTIMA-R. The results of the estimated total ambient dose equivalent, as well as the ambient dose equivalent rate for different flights, applying a typical flying level and constant atmospheric conditions, are presented for the first time. This study is carried out for different phases of solar activity for the time period from 1996 to 2019, which includes the two recent Solar Cycles 23 and 24.