© 2015 Elsevier Ltd. The growing interest in the use of offshore platforms in deeper waters and harsher environments, as well as the desire to extend the operation of existing structures beyond their design lives, is increasing attention on the assessment of the response and failure of these units under extreme storm loading. Such assessments of dynamically sensitive structures are complicated by their dynamic response combined with the random nature of extreme waves. This paper proposes a practical method for the estimation of (i) the extreme response statistics and (ii) the probability of failure of dynamically sensitive offshore structures in a given sea-state. The proposed method accounts for the random nature of a sea-state by the structured use of multiple Constrained NewWaves in combination with the Monte Carlo method. Analyses of a sample mobile jack-up structure show that the probability of failure can be efficiently calculated for even the most nonlinear and dynamically responsive offshore structures.