This paper presents a cross spectral stochastic analysis methodology for the determination of the combination of global wave-induced dynamic loads by taking into account uncertainties associated with the wave heading, the joint probabilities of the wave environment and the correlations between different global wave-induced dynamic loads. The methodology considers the use of bivariate probability density functions (the cross-spectral probabilistic approach) or the co-variances of two random variables with their associated derivatives (the cross-spectral Hamilton's method) and assumes only rigid body hydrodynamic actions under steady forward speed conditions. The design extreme values of principal global wave-induced load components and their combinations for a container ship progressing in irregular seaways are predicted using these two cross-spectral methods together with the short-term and long-term statistical formulations. It is shown that in general terms both cross-spectral analysis methods can be employed to assess the effects of loads in ship design and reliability analysis. However, the cross-spectral Hamilton's method predicts slightly higher load combinations than the cross-spectral probabilistic approach.