The operating environment of tidal stream turbines is random due to the variability of the sea flow (turbulence, wake, tide, streams, among others). This yields complex time-varying random loadings, making it necessary to deal with high cycle multiaxial fatigue when designing such structures. It is thus required to apprehend extreme value distributions of stress states, assuming they are stationary multivariate Gaussian processes. This work focus on such distributions, addressing their numerical simulation with an analytical description. For that, we first focused on generating one-dimensional Gaussian processes, considering a band-limited white noise in both the narrow-band and the wide-band cases. We then fitted the resulting extreme value distributions with GEV distributions. We secondly extended the generation method to the correlated two-dimensional case, in which the joint extreme value distribution can be obtained from the associated margins. Finally, an example of application related to tidal stream turbines introduces a Bretschneider spectrum, whose shape is commonly encountered in the field of hydrology. Comparing the empirical calculations with the GEV fits for the extreme value distributions shows a very well agreement between the results. Nomenclature Acronyms AR = Average Random EV D = Extreme Value Distribution GEV = Generalized Extreme Value IFFT = Inverse Fast Fourier Transform MA = Moving Average PSD = Power Spectrum Density Operators arg [•] = argument of the complex number • E [•] = statistical expectation of • Prob [•] = probability of the event •

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