This paper utilises two different computational methods to investigate the characteristics of a supersonic impinging jet at non-dimensionalised nozzle-to-wall distances (Zn/DZn/D) of 1.5 and 2.5 with the impinging angles from 0° to 45°. The static Smagorinsky subgrid-scale model was chosen for the LES and the two equation k–∊k–∊ turbulence model for the RANS. Computational parameters applied in the simulations emulated the experimental setup conducted by Risborg (2008). From the results obtained, both methodologies were able to predict the location of the first shock cell fairly accurately when compared to the steady-state shadowgraph images of Risborg (2008). However, the intensities of the shocks were significantly different between the two numerical methods, with the RANS underestimating the value of the density gradients at the shocks. The pressure distribution near the impinging plate have been investigated and found to differ between the RANS and the LES for small impinging angles (0° and 10°) when Zn/D=1.5Zn/D=1.5. In addition, the RANS data was not able to capture the recirculation zone for Zn/D=1.5Zn/D=1.5 and 0°0°. The instantaneous velocity fluctuations and temperature contours of the LES were also plotted to visualise the shear layer instability and also the chaotic nature of the supersonic jet. For Zn/D=2.5Zn/D=2.5 and 0°0°, the jet experiences high velocity fluctuations as the configuration causes the axially flapping instability. Overall, there are discrepancies between the RANS and LES but both are able to capture the key averaged flow features of the supersonic impinging jets.