There has recently been an interest in the methodology for synthesizing multi-directional random sea states. Several authors have reported that the wave generator was derived for both single and double summation models of the wave generation. To simulate irregular waves with directional spectrum, the authors studied the characteristics of directional waves generated in two models numerically and experimentally. Various alternatives for generating the fundamental wave trains areinvestigated through numerical simulation and results do not show differences between single summation and double summation wave model.