The boundary element method is applied to acoustic radiation and scattering from three‐dimensional objects submerged in a perfect waveguide. To simulate an idealized shallow‐water environment, the top surface is assumed to be perfectly soft and the bottom surface perfectly rigid. The waveguide Green’s function is calculated by either the image solution at short ranges or the normal‐mode solution at long ranges. Empirical rules of thumb for determining the so‐called ‘‘long ranges’’ are given. Since computation of the Green’s function is very time consuming, a so‐called ‘‘Green’s‐function interpolation technique,’’ recently developed for multifrequency acoustical analysis, is adopted to speed up the matrix formation procedure. It is found in many cases that the total CPU time is reduced to only one third of the conventional integration approach. The use of an improved CHIEF method to overcome the well‐known nonuniqueness difficulty at certain fictitious eigenfrequencies is also explored. An estimate of the matrix condition computed from a QR‐decomposition least‐squares solver is used to monitor the quality of the CHIEF solution.