The paper describes a method for stochastic representation of the hydrodynamic drag forces on offshore structures subjected to irregular waves. It is shown that, for the case of zero current, it is possible to construct a genuinely quadratic representation of the drag force which reproduces the statistical properties of the standard formulation of the drag force very closely, and which at the same time has sufficient flexibility to ensure a spectral density that accurately approximates the desired force spectrum. The distinct advantage of the new representation is that it brings dynamic analysis of extensive linear structures back into the frequency domain.