Uniform asymptotic approximations to the analytic solution for the acoustic field of a cw point source in an ideal wedge [M. J. Buckingham, Proceedings of the NATO Advanced Research Workshop on Hybrid Formulation of Wave Propagation and Scattering (Nijhoff, Dordrecht, The Netherlands, 1984), pp. 77–105] and to the approximate solution in a penetrable wedge [M. J. Buckingham, J. Acoust. Soc. Am. 82, 198–210 (1987)] are obtained by a stationary phase method (SPM). Comparisons of the solutions are made. Very good agreements are found in the bright zones, the caustics, and the shadow zones of the sustained normal modes in small angle wedges, provided that the source is at a range that is not shorter than the range at which the lowest mode can be excited, or the source and the receiver are well separated. One of the major advantages of the present representations is that, in comparison with numerical integration, the results can be generated rapidly with a satisfactory accuracy.