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This work deals with deep and ultra-deep waters installation by the so-called “J-Lay” method, which consists in laying submarine pipelines with a straight stinger at near-vertical angles. A hierarchy of simple analytical models is proposed starting from the classical catenary and enriching it to overcome its drawbacks. A novel approach for detecting the boundary layer phenomenon is proposed, and constitutes the base of two of the developed models. All models are compared with each other and with the results of refined numerical simulations in a case of practical interest. In the considered examples the stiffness of the soil has scarce influence, while the boundary layer phenomenon is very important and detected correctly, both from a qualitative and quantitative point of view, by the second class of proposed models.