A model has been developed to calculate extreme responses of turret moored ships. The responses are expressed in terms of the environmental parameters: waves wind and current. Motions in the horizontal plane, surge, sway and yaw, are analyzed statically and dynamically. The static analysis resolves the equilibrium position and heading about which the vessel oscillates. The dynamic analysis is a probabilistic one based on the first-order second-moment method. The frequency components of the ocean surface and turbulent wind processes, and their Hilbert transforms are transformed into a standardized form. A response, such as vessel offset, can be expressed in terms of the standardized variables. A constant value of that response then defines a limit state, a surface in the unit-variance normal space of the standardized variables. By an iteration process, we find the response corresponding to a prescribed probability of exceedance. The point on the limit state surface with the highest probability is the "design point". This qives the combination of wave and wind most likely to generate the extreme response.The set of wind gust and wave components that occasioned the design-point-response can be retrieved, and together constitute metocean histories, "designer wave," that may be used for further design or analysis. The algorithm is implemented in a program called TURRETDYN, which requires some time to find convergence in its iteration, Dut substantially less than its time domain counterpart. The results are compared with an existing time domain simulation program called DYNFLOAT The project essentially demonstrates the applicability of this probabilistic method, particularly for preliminary evaluation and as a means to generate extreme-response statistics and designer waves.