Numerical calculations of the response of an aluminum target impacted by an aluminum flyer driven by an intense laser are presented. The state of the accelerated flyer and the characteristics of shock wave propagation in the target are described in detail. If the parameters of laser and flyer-target structure are selected reasonably, an approximately symmetric impact can be realized between the flyer and the target, also the shock wave in the target has a wide stable range. Therefore the absolute measurement for the equation of state (EOS) can be almost achieved in laser EOS experiments with the bothside-step-target of suitable thickness.