A collisionless Weibel-instability mediated shock in a self-generated magnetic field is studied using two-dimensional particle-in-cell simulation [Kato and Takabe, Astophys. J. Lett. 681, L93 (2008)]. It is predicted that the generation of the Weibel shock requires to use NIF-class high-power laser system. Collisionless electrostatic shocks are produced in counter-streaming plasmas using Gekko XII laser system [Kuramitsu et al., Phys. Rev. Lett. 106, 175002 (2011)]. A NIF facility time proposal is approved to study the formation of the collisionless Weibel shock. OMEGA and OMEGA EP experiments have been started to study the plasma conditions of counter-streaming plasmas required for the NIF experiment using Thomson scattering and to develop proton radiography diagnostics.