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Coda-Q is a stochastic parameter reflecting the heterogeneities of medium that seismic waves travel through. We investigate a relationship between crustal stress field and the coda-Q. In this study we employ a 2-D Finite Different Method to calculate seismic wave propagation through the lower and upper crust. We confirmed that the coda-Q would vary with the stress loaded to an elastic medium using the numerical simulation. The coda-Q roughly shows a proportional relationship with magnitude of the stress. We also confirmed that the upper crust, where consists of a crack-rich medium, affects the coda-Q dominantly. Next, a relationship between coda-Q obtained from actual seismic records and crustal strain obtained from GPS data is examined, and they mark high correlation coefficient. Also we revealed that coda-Q changes according with the stress change before and after a large earthquake from the observation around Tohoku area in Japan.