A first Design Study Report has recently been completed [1] for the Linac Coherent Light Source (LCLS), a proposal to build an x-ray Free Electron Laser (FEL) at the Stanford Linear Accelerator Center (SLAC) as a single pass SASE (Self-Amplified Spontaneous Emission) amplifier. The proposal includes the use of a very low emittance electron beam accelerated up to 15 GeV by the last third of the SLAC linac to produce sub-picosecond x-ray pulses with high brightness and full transverse coherence in a 112-meter long undulator. Many aspects of the FEL design have been analyzed with FEL simulation codes. The paper discusses some of the results of these aspects, i.e. temporal x-ray pulse structure and power sprectrum, trajectory errors and effects of undulator beam tube wakefields.