This paper describes the motivation and process taken for developing an acceleration time history that has a shock response spectrum that matches the MIL-STD 810 defined shock response spectrum. The mathematics from the ISO standard 18431-4 are presented, as well as the procedures and graphs from the MIL-STD. The time history is synthesized from a sum of basis-functions, parameterized by variable amplitudes and delays. An optimization routine then modifies an array of these optimization parameters to find a time history that has a shock response spectrum that matches a reference shock response. All figures are presented in Appendix A for clarity. The equations developed and computer code written to perform this task are explained, and the full code is provided in Appendix B.