Nonlinear acoustic waves caused by an infinitely wide plate oscillating in its normal direction and propagating into a semi-infinite expanse of a rarefied gas are investigated numerically on the basis of a model Boltzmann equation and of the compressible Navier-Stokes equations with the correct temperature jump condition on the oscillating plate.The long-time behavior of the solution,including the attenuation of the waves and the creation of the acoustic stream,is obtained accurately.