Regional water resources management generally requires knowledge of multisite streamflows which exhibit random, yet spatially and temporally correlated, variabilities. The complexity of such correlated randomness makes decision-making for water resources management a difficult task. With presence of uncertainties in space and time, risk-based decision making using stochastic models is sought after. In this study we propose a spatiotemporal stochastic simulation model for multisite streamflow simulation. The model is composed of three components: (1) stochastic simulation of bivariate non-Gaussian distributions, (2) anisotropic space-time covariance function which characterizes the spatial and temporal variations of multisite ten-day periods (TDP) streamflows, and (3) Monte Carlo spatiotemporal simulation of streamflows. The model was applied to the Chia-Nan Irrigation District in southern Taiwan for a multisite spatiotemporal ten-day-period streamflow simulation. Through a rigorous evaluation, the proposed spatiotemporal model is found capable of preserving not only the marginal distributions but also the spatiotemporal correlation structure of the multisite streamflows. An example application which demonstrates utilization of the proposed model for irrigation water shortage risk assessment is also presented.