A probabilistic model is developed to predict the deformation demand on wind turbine support structures due to the operation of the turbine, and wind and wave loading. An existing deterministic model is corrected by adding a correction term to capture the inherent bias and model error arising from an inaccurate model form or missing variables. The correction term and the model error are assessed using data obtained from detailed three dimensional nonlinear finite element analyses of a set of wind turbine systems considering different design parameters. Fragility of the support structure is then defined as a conditional probability of not meeting a specified deformation performance level. Existing simplified methods for the analysis of the support structure and foundation of wind turbines have limitations in the modeling of the nonlinear behavior of the foundations. Three dimensional nonlinear finite element analyses provide a more rigorous and accurate modeling of the soil mass, pile and their interaction, but they are computationally expensive and time consuming. The proposed probabilistic demand model provides an accurate framework for predicting the deformation of the support structure properly accounting for the underlying uncertainties, and for estimating the vulnerability of the wind turbine support structure without the need of conducting complicated nonlinear finite element analyses.