Abstract This paper proposes a methodology to obtain the transient response of structural system interacting with soil-foundation schemes supported by viscoelastic soils. The structure and soil are divided into sub-systems. The time domain solution for each subsystem is formulated by an appropriated methodology. The equations of motion of structure are solved by Newmark integration algorithm. The transient response of the soil is obtained by a convolution integral. The convolution integral uses transient impulse response of viscoelastic soils. Newmark and convolution algorithms are formulated as input and output schemes, which, in turn, are plugged to the time stepping iterative algorithm. The scheme is applied to vertical response of a dynamical system interacting with a massless foundation laying on a soil modelled as a three-dimensional homogeneous viscoelastic half-space. For two distinct external forces, the resulting coupled displacements, interface forces, errors and number of iterations within each time step are provided.