A method of laying a pipeline on the bed of a body of water includes constructing, on a laying vessel, a pipeline having pipe sections of a designated or given thickness, and thicker pipe sections distributed along the pipeline; moving the laying vessel forward and laying the pipeline in the body of water as the pipeline is constructed; and propelling a train, configured to plug the pipeline, in steps inside the pipeline laid on the bed of the body of water; the step travel of the train being related to the position of the thicker pipe sections, and to the touchdown point of the pipeline on the bed of the body of water.