This paper revisits the phenomenon of current blockage in offshore engineering. Standard current blockage theory was first developed by Taylor (1991) and is suited for grids of obstacles in steady flow when Morison drag is assumed locally. This is confirmed by analysis of the published experimental data on drag forces for several examples of multiple grids of obstacles in steady flow. A more complex analytical model is derived to account for the considerable extra blockage which occurs when a space-frame structure is exposed to regular waves and an in-line current. This new model is shown to be in excellent agreement with the experimental data of Allender and Petrauskas (1987) for steady current superimposed with regular waves, both incident on a model of a Gulf of Mexico jacket. In contrast, both the original unblocked version of the Morison equation and the Morison equation assuming just steady current blockage (as in API RP2A) over-estimate the measured forces.