This doctoral dissertation entitled "Model for determining the acceptability of maritime navigational risks" systematically investigates the risks of vessels grounding and the criteria by which to evaluate these risks. For the purpose of obtaining the acceptable risk of grounding, a model was made that allowed the variation of parameters. The obtained results are used for grounding risk assessment. In determining the boundary parameters that define safe navigation, the parameters of safe navigation when all the ship's systems were working properly were explored separately from the case when during a voyage an extraordinary event occurs. By analysing expert and scientific literature, conducting interviews with active seamen and pilots, and research with navigation simulators, the coefficients were defined for determining the width of the waterway which can be considered safe for ship navigation, assuming that all on-board systems are working properly and that the ship is also managed by a helmsman who acts as "good seamanship". For purposes of conducting research on the risk of grounding due to an emergency event onboard, various scenarios were defined. To create a track model, an Euler spiral/clothoid was chosen. By modifying the parametric clothoid equations, a curve was obtained which very well approximated the curve of a turning ship. Furthermore, the speed change model was developed, which can show a change of speed at any point of the ship turning curve when the rudder deflection was constant, and the engine was stopped. The designed models were tested in 60 scenarios, in accordance to which research on the navigation simulator has been carried out. In order to show the possible consequences of grounding papers and models relating to the mechanical damage to the ship upon grounding were analysed. The obtained results were used to achieve the primary objective of this dissertation, which is the model for determining the acceptability of maritime navigational risks. For this purpose, a model based on the extent of damage to the ship is used. For the purposes of determining the parameters which will enable the determining of the extent of grounding consequences in various scenarios, a simulation model was developed. Results and findings reached in this paper allow the evaluation of decisions to be taken at national or local level.