This study investigates spatial cross‐correlation models for two sets of vector intensity measures (IMs) considering the influence of regional site conditions. The first set of the vector IM consists of the peak ground acceleration, Arias intensity, and the peak ground velocity; the second set is for spectral accelerations at multiple periods. Geostatistics analyses are performed using 2686 strong‐motion data from 11 recent earthquakes that occurred in California, Japan, Taiwan, and Mexico. The results indicate that the spatial cross correlations of the vector IMs are strongly influenced by the spatial distribution of regional site conditions, which can be quantified using RVS30, the correlation range of shear‐wave velocity in the top 30 m. The linear model of coregionalization is proposed to construct a permissible spatial correlation model, and the short‐range and long‐range coregionalization matrices is specified to vary linearly with RVS30. The proposed model demonstrated excellent performance in quantifying the influence of regional site conditions on the spatial cross correlations for the vector IMs, meanwhile the model guarantees a positive‐definite covariance matrix for any reasonable value of RVS30, a mathematical condition required for stochastic generation of the spatially correlated random fields. The spatial cross‐correlation models proposed in this study can be conveniently used in regional‐specific seismic risk analysis and loss estimation of spatially distributed infrastructure using vector IMs.