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Calculation of impedance function is a mixed boundary value problem, which is changed to a Neuman problem by using a functional expansion of stress distributions. The problem is, then, solved using integral transforms (Hankel transform for circular foundations) and the impedance function is obtained in terms of an integral that is resulted from Hankel inverse transform. This integral cannot be solved analytically and, therefore, is solved numerically and the impedance function is obtained. The variation of impedance function with dimensionless frequency is presented for some isotropic or transversely isotropic materials with different poisons ratios. It can be seen that anisotropy has a great effect on impedance functions and this effect increases as the anisotropy ratio increases.