Abstract Probabilistic descriptors are developed for the response of a SDOF system subjected to Morison-type wave forces. The first section provides a method for predicting the non-normality of the response in terms of its skewness ψ and coefficient of excess δ, based on a new separability assumption. The second part discusses a rule of estimating the probability density function of the responses utilizing the above two parameters. The third part extends this rule for the prediction of the mean upcrossing rate. Finally the estimation of the distribution of peaks and of the mean fatigue damage rate in section four, completes this study. The approximate methods mentioned above have been compared with exact theoretical results for the quasi-static response and with simulation studies for the dynamic response.