New techniques are introduced into the Bayesian modeling procedure to estimate directional wave spectra based on ship motion data. In this proposed method, the triple-valued function problem in following seas is strictly taken into account, and the optimum solution is obtained from the stochastic viewpoint. Using the estimated directional wave spectrum, it is shown that the future states of ship motions and longitudinal bending stresses can be evaluated based on the assumption of linear responses. Onboard experiments were carried out to examine the reliability of the proposed method. Comparisons between the results of the proposed method and onboard experiments show good agreements.