In the past many researchers studied dynamic stiffness and damping coefficients of surface and embedded rigid foundations of arbitrary shapes in the elastic homogenous half space. Dynamic stiffness and damping coefficients were obtained by using regularly shaped foundations instead of arbitrarily shaped ones. Obviously, the calculating methods were not perfect. In addition, the two parameters mentioned above were calculated only in the case of a single foundation. But the cases of two or more foundations were not presented because the interactions between foundations were not considered in all present papers. This paper eliminates two faults named above by using the assumption of the plane strain and of dynamic foundation-soil interaction factors. The calculating method of dynamic impedances presented by the paper proved to be accurate and practical.