An unstructured mesh Navier-Stokes solver employing a Maxwell slip boundary condition was developed. The present flow solver was applied to the simulation of flows around an axisymmetric hollow cylinder in a Mach 10.4 freestream, known as Calspan-UB Research Center (CUBRC) Run 14 case, and the velocity slip and the temperature jump on the cylinder surface were investigated. The effect of tangential momentum and thermal accommodation coefficients used in the Maxwell condition was also investigated by adjusting their values. The results show that the reverse flow region is developed on the body surface due to the interaction between the shock and the boundary layer. Also, the shock impingement makes pressure high. The flow properties on the surface agree well with the experimental data, and the velocity slip and the temperature jump vary consistently with the local Knudsen number change. The accommodation coefficients affect the slip phenomena and the size of the flow region. The slip phenomena become larger when both tangential momentum and thermal accommodation coefficients are decreased. However, the range of the reverse flow region decreases when the momentum accommodation coefficient is decreased. The characteristics of the momentum and thermal accommodation coefficients also are overlapped when they are altered together.