Multivariate normality of logarithmic intensity measures (IMs) is conventionally assumed in earthquake engineering applications. This article introduces a vine copula approach as a useful tool for multivariate modeling of IMs. This approach provides a flexible way to decompose a joint distribution into individual marginal distributions and multiple dependences characterized by a cascade of bivariate copulas (pair‐copulas), whereas the conventional multivariate normality can be considered as a special case of the vine copula model. Based on the Next Generation Attenuation‐West1 database and various combinations of ground‐motion prediction equations (GMPEs), the optimal dependence structures among peak ground acceleration, peak ground velocity, and Arias intensity, as well as that for spectral accelerations at four periods, are identified. The joint normality assumption for the two vector sets of logarithmic IMs is examined from the perspective of copula theory. The results illustrate that the normality assumption is generally adequate for bivariate IMs but may not be optimal for multivariate IMs. Using the same set of GMPEs (developed by the same researchers) may improve the joint normality for logarithmic IMs. Furthermore, the impact of dependence structures among IMs on probabilistic seismic slope displacement hazard analysis is explored. The results indicate that using the same Pearson correlation coefficients but different dependence structures for IMs produces different hazard results and this difference is generally enlarged with increasing hazard levels. As hazard difference from different dependence structures is generally not significant, the multivariate normality distribution for logarithmic IMs is judged to be an acceptable assumption in engineering practice. Alternatively, engineers may make a choice between the joint normal distribution and the vine copula tool depending on the specific situation because of the better generality of the latter.