A large number of containers is lost every year from ships along shipping routes. Even though the economic losses are in most cases covered by insurance, the containers drifting in sea may compromise the safety of navigation. Moreover, there can be serious consequences for the environment, in terms of pollution. All the reported losses were caused by extremely violent motions of containerships, due to adverse weather conditions. This pointed out the need of further researches on safer container shipping, through heavy sea states. The accurate determination of design accelerations and loads on container stacks are of prime importance for safety. This paper proposes a realistic numerical modeling approach of the critical ship motions, including the pertinent nonlinearities. A method to evaluate a map of the dynamic loads along the container arrangement is presented. This calculation is based on a fine description of the acceleration distribution on the ship. Area exposed to higher accelerations will be highlighted. The method can be used to guide the design of lashing systems for containerships to sustain the actual accelerations and forces. Sample calculation of the forces acting at the container locks is provided for a conventional and a non-conventional container arrangement on board.