Various methods have been developed to determine the dynamic stiffness of different types of foundations and to evaluate the effective foundation input motion applied to the structure during seismic excitation. The exact solutions for footings response on soil layers can be derived by employing complicated analytical solutions and numerical techniques such as finite element method, boundary element and scaled boundary element method. This accurate methods in addition to theoretical complexity and time-consuming, require to Fourier transformation to the frequency domain. However, practicing engineers prefer to perform the dynamic analysis in the time domain. Time domain analysis provide physical insight and makes it possible to consider the non-linear behavior of the structure. To compute the dynamic response of foundations for an arbitrary excitation defined in time domain, at beginning of the analysis the Fourier transformation of the load to the frequency domain is performed. The footing response is obtained in the frequency domain and should be the transformed back into the time domain at the end of analysis using inverse Fourier transform. In this indirect procedure, as an alternative to the rigorous approach, it is convenient to idealize the soil by the semi-finite truncated cone models representing the infinite nature of supporting soil. The cone model approach initially developed in the frequency domain. In this method, strength of materials theory for cones is employed (‘plane sections remain plane’). The reflection and refraction of waves at the material discontinuities such as a stratum on a half-space, that leads to frequency-dependent reflection coefficients for cones, bars and beams, is exactly considered. Cone models are potentially attractive because the one dimensional wave equation for cones can be solved directly in the time domain. Since the reflection coefficient is a function of the frequency, therefore, the reflection coefficient at the low frequency limit and high frequency limit asymptotes to a constant, being a function of the material properties of two neighboring layers at the interface. Accordingly, if one of these limits used as an approximation, a frequency-independent formulation of the wave mechanisms at the discontinuity of materials achieves, which permits to be implement the dynamic analysis directly in popular time domain without any transformation to and from the frequency-domain. The method can be extended for layered soils. The wave propagation mechanism across a cone segment and the wave transferring at material discontinuity leading to refracted and reflected waves is analogous to that in the frequency domain. In order to implement the dynamic soil-structure interaction analysis in the time domain the interaction forces of the soil must be expressed in the time domain. The formulation directly in the time domain has been obtained for the translational degree of freedom for a shallow foundation on a layered half-space, while the wave pattern in the time domain is not studied for a rocking degree of freedom. The purpose of this thesis is to obtain equations for the direct analysis of the interaction of soil-structure for the rocking degrees of freedom in the time domain using the theory of cones. Key Words : Soil-structure interaction analysis, Cone models, Time domain, Rocking degree of freedom, Layered half-space, Dynamic stiffness.