This paper presents three-dimensional elasto-dynamic infinite elements for the three-dimensional soil-structure-interaction problem in a multi-layered half-space. Five kinds of infinite elements are developed in Cartesian coordinates using approximate expressions of multiple wave components for the wave functions in the exterior far-field soil region. They are horizontal, horizontal-corner, vertical, vertical-corner and vertical-horizontal-corner elements. Modified wave numbers are introduced to make the wave lengths in the original radial coordinates fit into the Cartesian coordinates. The elements can be used for the multi-wave propagating problem. Numerical example analyses are presented for a rigid disk, rectangular footings, and an embedded caisson on homogeneous and layered half-spaces. The numerical results obtained show the effectiveness of the proposed three-dimensional infinite elements. (c) 2007 Published by Elsevier Ltd.