A hypersonic monoatomic gas (argon) flow around a hollow cylinder flare was numerically simulated for low-to-moderate Reynolds numbers. A shock wave induced by the flare causes the formation of a separation region, and flow rarefaction near the leading edge affects the separation extent. The continuum (Navier-Stokes equations) and kinetic (the DSMC method) approaches were used to study the influence of the Mach number and wall-to-freestream temperature ratio on the flow structure and separation. To take into account rarefaction effects, slip boundary conditions are used for the Navier-Stokes solver.