A uniform asymptotic solution is presented for sound propagation from a constant frequency point source in shallow water whose depthH(r) decreases monotonically with cylindrical distancer. The water has constant sound speedc1and density ρ1; the bottom fluid extends indefinitely in depth and has sound speedc2and density ρ2, wherec2>c1. The interface depth has constant valueH0up to ranger0and thereafter decreases linearly to zero. The solution appears as a sum of modal terms, each such mode eventually encountering a critical depthHc(n) (at which modal phase velocity equalsc2) at a critical rangerc(n). A previously derived local solution for a modal term near its critical range is modified such that it automatically reduces to the adiabatic mode solution at nearer ranges and such that it is valid at arbitrary distances beyond the critical range. Bulk attenuation is incorporated into the model using an appropriate modal average over depth. Numerical results are compared with four parabolic equation computations supplied by Jensen. In these four cases only single mode propagation is considered andr0is 0. The two theories agree well, with discrepancies typically less than 1 dB. Additional comparisons with parabolic equation computations (simultaneous propagation of three and two modes) presented by Jensen and Kuperman [J. Acoust. Soc. Am.67, 1564–1566 (1980)] show comparable agreement, but for the higher modes there are marked discrepancies in the directions at which sound is beamed into the bottom fluid from regions encompassing those mode’s critical ranges. This is attributed to the progressive deterioration of the present theory with increasing mode number.