The runway excursions are defined as the exit of an aircraft from the surface of the runway. These excursions can take place at takeoff or at landing and consist of two types of events: veer off and overrun. This last one, which occurs when the aircraft exceeds the limits at the end of the runway, is the event of interest in the current study. This chapter aims to present an accident model with a new approach in aeronautical systems, based on the tasks of the pilots related to the operational procedures necessary for the approach and landing, in order to obtain the chain of events that lead to this type of accident. Thus, the tree-network overrun model (TNO model) was proposed, unlike most traditional models, which consider only the hardware failures or which do not satisfactorily explain the interrelationship between the factors influencing the operator. The proposed model is developed in a fault tree and transformed into a Bayesian network up to the level of the basic elements. The results showed the qualitative model of the main tasks performed by the pilots and their relation to the accident. It has also been suggested how to find and estimate the probability of factors that can impact on each of the tasks.