The increased demand for transport capacity led to new hull designs with a large bow flare that are able to carry more containers. These new hull shapes influence the ship stability and may lead to large roll angle amplitudes, which lead to high accelerations and thereby to a high safety risk for human life, ship and cargo. To be able to predict or prevent large roll angles and roll acceleration, it is important to understand the physical principals of roll motion and especially roll damping. The assessment of dynamic stability of ships in the early design phase is needed. In today’s naval engineering practice, the roll motion of a ship is computed with computational methods based on the potential theory. These methods are sufficiently fast for ship design purposes. However, they lack the ability to predict viscous roll damping, which has to be determined with other means such as model tests, viscous field methods or empirical prediction methods. Model tests, in turn, are costly, time consuming and suffer from scale effects on the roll damping. Empirical methods such as the Ikeda method are also restricted in their use, as their development was based on a restricted number of hull shapes (e.g. slender bodies) and may not be valied for modern ship designs. The demand for a roll damping prediction method and the described deficit in the current roll damping assessment methods led to the two main objectives of this thesis: An in-depth analysis of the roll damping mechanisms and identification of the influencing factors of the roll damping coefficients of modern hull shapes. Secondly, the development of a mathematical model for the roll damping prediction of modern ship hulls. For this purpose, numerical roll damping simulation were conducted for a systematic variation of hull shapes. The resulting time series data was then used in a nonlinear regression analysis to derive the mathematical roll damping prediction model. In order to apply a consistent methodology for this pro- cess, a computational framework was implemented, that incorporates all the numerical tools, that were used. The result from this development is a database with the roll damping coefficients for a series of hull shape variations, a systematically evaluated roll damping model and a prediction method for the roll damping behavior of new hull designs.