This paper investigates the self-similarity properties in the far downstream of high Reynolds number turbulent wake flows. The growth rate of the wake layer width, ; the decaying rate of the maximum velocity defect, ; and the scaling for the maximum mean transverse (across the stream) velocity, Vmax, are derived directly from the self-similarity of the continuity equation and the mean momentum equation. The analytical predictions are validated with the experimental data. Using an approximation function for the mean axial flow, the self-similarity analysis yields approximate solutions for the mean transverse velocity, V, and the Reynolds shear stress, . Close relations among the shapes of U, V, and T are revealed.