The structure of the collisionless electrostatic shockwave (CES) and the process of the ion acceleration by shock wave are investigated with a series of two dimensional particle-in-cell (PIC) simulations. It is found that only ions satisfying some criteria can be accelerated due to the bipolar electric field in the shock wave front. A comparative investigation of the ion acceleration process by shock wave and solitary wave has been made. Only ions located in the sheath can be accelerated by the solitary wave. We also compare the shock wave for different laser intensities and different plasma densities. The ion energy spectrum of the shock wave has a platform. It can be used to ignite as the ignition material.