This paper deals with the dynamic stiffness rigid strip footings resting on irregular soil stratum. Above the fundamental frequency of soil stratum, the change in the inclination of the rigid bed-rock causes the variations of dynamic stiffness with frequency to shift, leading to significant differences at certain ranges of frequencies for shallow stratum; however, such differences become less for deeper soil stratum. On the other hand, if only the soil layers are inclined, no significant shift in the variations of dynamic stiffnesses with frequency is observed over the range of frequencies considered. The increase in the angle of inclination of soil layers leads to a reduction in the real stiffnesses of all modes of motion and the damping of vertical stiffness, while the opposite trend is observed for the damping of swaying and rocking stiffness.