An axisymmetric supersonic screeching jet is numerically simulated to examine the length scales of screech frequency as well as screech tone generation mechanism. The axisymmetric Reynolds-averaged Navier-Stokes equations in conjuction with a modified Spalart-Allmaras turbulence model are employed. It is demonstrated that the axisymmetric jet screech tones can be simulated correctly and the numerical results are in good agreement with the experimental data. Instability waves, shock-cell structures and the phenomena of shock motion are investigated in detail to identify the screech tone generation mechanism. Shock spacings and standing wave length are analyzed to determine the dominent length scale crucial to the screech frequency formulation.