Abstract: For micro-scale gas flows, the Navier-Stokes equations with first-ordervelocity slip boundary conditions give results that agree with experimental data in the slipregime, but differ obviously in the transitional regime. Second-ordervelocity-slip boundary conditions were introduced to improve the performanceof the Navier-Stokes equations in the transitional regime. This paperconsiders two-dimensional gas flows through microchannels for which theNavier-Stokes solutions based on different second-order velocity-slipboundary conditions suggested by Cercignani, Deissler, Beskok andKarniadakis, respectively, are compared with the kinetic results given bythe information preservation (IP) method, the direct simulation Monte Carlo(DSMC) method, and experimental data. It is shown that the Cerciganani modelperforms best among the three second-order models we examined, and its massflow rate agrees with the DSMC and IP results even at the Knudsen number of0.4. However, a careful examination of the slip velocities and velocitydistributions at and around the channel surfaces given by the Cercignanimodel demonstrates that they considerately deviate from those given by theDSMC and IP methods at the Knudsen number of 0.1, that is generally regardedas a critical value to divide the slip and transitional regimes.