We have developed a fully coupled categorical-multivariate continuous stochastic inversion with a combined petro-elastic model and convolution. The new multivariate stochastic seismic inversion approach simulates multiple reservoir properties simultaneously and conditions them to the well and seismic data at the same time through the close integration of multivariate geostatistical modeling and stochastic inversion. This approach combines a trace-by-trace (column-wise) adaptive sampling algorithm with multivariate geostatistical techniques to select reservoir properties that match the seismic data. The adaptive sampling method uses an acceptance-rejection approach to condition geostatistical models to the well and seismic data. The adaptive sampling algorithm defines a practical stopping criteria based on the inherent uncertainty due to modeling assumptions and the size of the uncertainty space. This technique samples the realizations inside the space of uncertainty; the number of realizations attempted increases with the size of the space of uncertainty. Characterizing multiple reservoir properties simultaneously through the close integration of seismic inversion and multivariate geostatistical techniques leads to improved high-resolution reservoir property models that reproduce the original seismic data. A case study is considered to compare the proposed stochastic inversion approach with the conventional methods. The case study represents multivariate stochastic inversion provides high-resolution facies and reservoir physical properties simultaneously that reproduce the original seismic data within quality of data better than the other approaches.