Who would have foreseen 40 years ago the launching of an 18 000 TEU container ship? The unprecedented growth of such ships presents an increasing challenge for port infrastructure planners. The paper concludes that during the next 20 years, the growth of container ships will depend on factors related to supply and demand, and to external factors. These factors will be defined as the constraints. These constraints have been determined using a semi-quantitative methodology, which starts with a pre-foresight analysis, then continues with a foresight analysis based on the judgement of experts, using the Delphi technique. The experts' judgement, with a vision shared by 82% of those participating, establishes that the trend for growth in the size of container ships will depend principally on the following factors: economic growth, port access channels, berth depth alongside, air draft, and limitations in natural channels and straits. This result, representing the experts' group vision, is offered as a basis for the establishment of long term policies.