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It is well known that biological tissue adapts to changes in mechanical loading. The stress level in the myocardium is an important factor in evaluating the cardiac tissue. For example, it may be an indicator of the metabolic rate of cardiac cells. But measuring the stress level in living tissue is very difficult. The deformations of the left ventricle (LV) can be obtained from 3D tagged MRI or image warping. To calculate the stress distribution in the LV, the mechanical properties of myocardium still must be determined. In this paper, we studied the feasibility to use a finite element (FE) model of the LV to estimate the material constants for Humphrey's model of passive cardiac tissue from cine MRI data. In our simulations, the target strain-map was generated by running the forward FE model of the LV with known material constants. The target strain-map was compared with current strain-map and objective functions were defined as the discrepancies between them. Newton-Raphson's method was used to minimize the objective functions iteratively.