This article elaborates on an extension to the classical stiffness matrix method to obtain the Green's functions for two-and-a-half dimensional (2.5D) elastodynamic problems in homogeneous and horizontally layered half-spaces. Exact expressions for the three-dimensional (3D) stiffness matrix method for isotropic layered media in Cartesian coordinates are used to determine the stiffness matrices for a system of horizontal layers underlain by an elastic half–space. In the absence of interfaces, virtual interfaces are considered at the positions of external loads. The analytic continuation is used to find the displacements at any receiver point placed within a layer. The responses of a horizontally layered half-space subjected to a unit harmonic load obtained using the present method are compared with those calculated using a well-established methodology, achieving good agreement