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Mechanical properties of tissues in terms of elasticity and viscosity provide us useful information which may be used in detecting tumors. Shear wave imaging (SWI) is a new method to quantify tissue elasticity by estimating the parameters of the complex shear modulus (CSM). The shear wave is generated by a vibrating needle at a certain frequency. In fact, CSM is a function of the vibrating frequency. Therefore, in this paper, a frequency dependent investigation of CSM will be carried in order to evaluate the estimation performance. The Extended Kalman Filter (EKF) is designed to estimate the CSM for both homogeneous and heterogeneous mediums. The root mean square (rms) error is used to evaluate the quality of the CSM estimation. Several tests were implemented to determine the range of vibrating frequency should be used for the good estimation.