The study of lunar plasma environment’s response to the extreme solar wind condition is the main subject of our investigation in this report. The computational model includes the self-consistent dynamics of the light (H_2+) and (He+), and heavy (Na^+}) pickup ions. The electrons are considered as a fluid. The lunar interior is considered as a weakly conducting body. The input parameters are taken from the ARTEMIS observations. The modeling demonstrates a formation of the various plasma structures near the Moon: (a) bow shock wave with split shock transition in case of extreme solar wind density and standard bulk velocity; (b) hyper-sonic/Alfvenic Mach cone in case of extreme solar wind bulk velocity and moderate solar wind density. The modeling shows a strong asymmetry in the solar wind ion VDF which connected with a plasma compression and ion reflection at the bow shock wave/Mach cone front.