The offshore Ocean Thermal Energy Conversion (OTEC) has great potential to provide clean energy in the inter-tropical zone. Its main technological barrier is the cold-water pipe (CWP) that upwells water from 1000 meters deep. The paper presents a theory developed specifically for OTEC to analyse the impact of waves and shear current on the CWP. In this theory, the CWP is modelled as a series of discrete beams, attached to a floating platform at its upper end and left free at its lower end. Little investigated in the hydrodynamics field, Lagrangian mechanics is innovatively used in the study. Comparisons with an acknowledged software (DeepLines™) show a similar magnitude of loads and displacement, making the model sufficiently accurate for a preliminary structural analysis. Therefore, this theory is validated as a solid basis to be completed by OTEC-specific applications, including inner flow studies.