This paper presents a bivariate regional frequency analysis applied to data of extreme significant wave heights and concurrent wave period over an area in the North Atlantic Ocean. It extends previous regional frequency analysis on significant wave height to the bivariate case where the joint distribution of significant wave height and zero up-crossing wave period are analysed. This is believed to be an important extension, as the joint distribution is typically needed for marine design and other ocean engineering applications. The analysis presented in this paper is based on a bivariate index-wave/period approach and assumes a common regional growth curve within homogeneous regions of the overall area. One of the main benefits of performing a regional frequency analysis as opposed to at-site analysis based on data from one location only is that more accurate predictions of extreme conditions can be obtained, due to the increased number of observations that will effectively be available. Moreover, results for locations within the regions where no observations are available can be obtained by interpolation of the index wave/period and utilizing the regional growth curve. This paper outlines the various steps and modelling choices involved in a bivariate regional frequency analysis and presents the results of such an analysis applied to 30 years of data covering the North Atlantic Ocean. Moreover, it is shown how environmental contours can be constructed based on the outcome of the bivariate RFA, corresponding to one particular definition of a bivariate return period.