A direct method for soil-structure interaction analysis in two-dimensional medium is presented in time domain, which is based on the transformation of the analytical frequency-dependent dynamic stiffness matrix. The present dynamic stiffness matrix for the far-field region is constructed by assembling stiffness matrices of the analytical frequency-dependent dynamic infinite elements, so that the equation of motion can be analytically transformed into the time-domain equation. An efficient procedure is devised to evaluate the dynamic responses in time domain. Verification of the present formulation is carried out by comparing the compliances for a strip foundation on a homogeneous and layered half-spaces with those obtained by other methods. Numerical analyses are also carried out for the transient responses of an elastic block and tunnel in a homogeneous and a layered half-space. The comparisons with those by other approaches indicate that the proposed time-domain method for soil-structure interaction analysis gives good solutions. Copyright (C) 2000 John Wiley & Sons, Ltd.