A solution for the surface displacements due to buried dislocation sources in a multi-layered elastic medium is found using the Haskell (1964) paper as a starting point and more importantly, for notation. Through the introduction of some simple matrix operations, the Haskell (1964) solution is made simultaneously more compact and computationally stable. Time histories are computed for a perfectly elastic medium by performing classical contour integration in the complex wavenumber plane. A new aspect in the evaluation of those contours is introduced because of the recognition of nonzero singularity contributions of the Hankel and modified Bessel functions at k = 0. Theoretical ground motion time histories are presented to show the usefulness of the formulation. The overall objective of this paper is to incorporate the modifications made since 1964 to the Haskell (1964) paper in an easily understandable, step-by-step development.