The Telescope Array (TA) collaboration has measured the energy spectrum of ultra-high energy cosmic rays (UHECRs) with primary energies above 1.6 x 10 super(18) eV. This measurement is based upon four years of observation by the surface detector component of TA. The spectrum shows a dip at an energy of 4.6 x 10 super(18) eV and a steepening at 5.4 x 10 super(19) eV which is consistent with the expectation from the GZK cutoff. We present the results of a technique, new to the analysis of UHECR surface detector data, that involves generating a complete simulation of UHECRs striking the TA surface detector. The procedure starts with shower simulations using the CORSIKA Monte Carlo program where we have solved the problems caused by use of the "thinning" approximation. This simulation method allows us to make an accurate calculation of the acceptance of the detector for the energies concerned.