The principle of arc shape waveguide all optical switch is introduced and the switching characteristic of this kind of switch on ideal Kerr substrate is simulated by finite difference beam propagation method (FD BPM).The non Kerr nonlinear optical response in the Kerr medium is analysised.The effect of nonlinear saturation and background absorption on the switching characteristic is simulated by BPM.The results of the simulation shows that either nonlinear saturation or background absorption can reduce the switching times and enhance the switching power of the switch.So the existence of non Kerr nonlinear response can deteriorated the switching characteristic of arc shape all optical switch.