The focus of this study is on estimating the multivariate extreme value distributions associated with a vector of mutually correlated non-stationary Gaussian processes. This involves computing the joint crossing statistics of the vector processes by assuming the crossings to be Poisson counting processes. A mathematical artifice is adopted to take into account the dependencies that exist between the crossings of the processes. The crux in the formulation lies in the evaluation of a high-dimensional integral, which can be computationally expensive. This difficulty is bypassed by using saddlepoint approximation. The developments are illustrated through two numerical examples and are validated using Monte Carlo simulations. In the second example, reliability analysis is carried out for a multiply supported pipeline on an offshore jacket structure subjected to wave loading using the proposed formulation. © 2016 Elsevier Ltd.