This paper presents a fully analytical solution, together with explicit expressions, for the steady-state response of a homogeneous 3D space subjected to a spatially sinusoidal, harmonic line load. In the literature, this problem is often referred to as the two-and-a-half-dimensional fundamental solution or two-and-a-half-dimensional Green's functions. These equations are of great usefulness in the formulation of 3D elastodynamic problems by means of integral transforms methods and/or boundary elements. The final expressions are validated here by applying the equations to the problem of a 3D point load, for which the solution is known in analytical form.