This article investigates economic and operational effects of introducing autonomous vessels to liner shipping networks. By the formulation of optimization models, we analyze how fleet configurations with vessels of different capacity affect the cost and service level of liner shipping networks in both static and dynamic settings. We implement the model in a data instance that extends a data instance on the Baltic trade from conventional to autonomous vessels. Our results show that the introduction of autonomous vessels might lead to cost savings of 7.1% with respect to the fleet of conventional vessels. The main savings come from lower time charter costs and lower bunker costs. The results also suggest that a fleet configuration combining large with small vessels perform better, because of its better ability to accommodate to the asymmetry of the trade. The implementation of a flexible sailing schedule in the dynamic setting might lead to a great increase in the service level of the network, but at the expense of an increase in costs.