In this study, time-dependent numerical analysis was carried out to investigate the plasma jet impingement on a flat plate, and a compressible form of two-dimensional inviscid gas dynamics equations were solved using the flux corrected transport algorithm. The mathematical modeling of Joule heating in the polycarbonate capillary bore and the mass ablation from the bore wall was incorporated in the numerical analysis and the series of computation was performed for three cases depending on the distance of the opposing plate from the capillary exit. The computational results reveal that the presence of the opposing plate does not affect the flow conditions inside the capillary when compared to the case of open-air plasma discharge. In the exterior region, the flow structure shows the typical supersonic underexpanded jet which consists of the strong Mach disk in front of the opposing plate and the barrel shock at the side of the jet. It is found that the shock evolution becomes more quasi-steady when the plate distance decreases. Also, the effects of the distance between the capillary bore exit and the opposing plate on the flow conditions along the opposing plate are investigated and the pressure variation on the plate shows more complicated interaction between the plasma discharge and the opposing plate when the location of plate becomes closer to the capillary exit.