To ensure acceptable operation and/or survival of floating structures in extreme conditions, nonlinear time-domain simulations are often used to predict the structural response at the design stage. An environmental contour (EC) is commonly employed to identify critical sea states that serve as input for numerical simulations to assess the safety and performance of marine structures. In many studies, marginal and conditional distributions are defined to construct bivariate joint probability distributions for variables such as significant wave height and zero-crossing period; then, environmental contours can be constructed using the inverse first-order reliability method (IFORM). This study adopts alternative models to describe the generalized dependence structure between the environmental variables using copulas; the Nataf transformation is also discussed as a special case. Environmental contours are constructed, making use of measured wave data from moored buoys. Derived design loads are applied on a semi-submersible platform to assess possible differences. In addition, the long-term extremes of the tension of the mooring lines are estimated, considering uncertainties in the structural response using a 3D model (that includes response variability, ignored with the EC approach) to help establish more accurate design loads using Monte Carlo simulation. Results offer a clear indication of the extreme response of the floating structure based on the different models.