AbstractA boundary element approach for time harmonic axisymmetric problems using the complete space point load fundamental solution is presented. The fundamental solution is integrated numerically along the azimuthal co‐ordinate of each axisymmetric element. To increase the accuracy of the numerical integration a simple co‐ordinate transformation is proposed. The approach is applied to the computation of the dynamic stiffness functions of rigid circular foundations on layered viscoelastic soils. Three different sites are considered: a uniform half‐space, a soil layer on a half‐space, and a soil consisting of four horizontal layers and a compliant half‐space. The numerical results obtained by the proposed approach for surface circular foundations are very close to corresponding published results obtained by different p