The determination of the continuous spectral contribution to the transmission loss in ocean acoustics can be very difficult. While it is applicable to very general sound‐speed profiles, a uniform asymptotic method, i.e., one that is valid as the proper modes pass through cutoff, is proposed and illustrated for the Pekeris model. The method exploits the fact that there are singularities near the integrand of an integral representation of continuous spectrum and that these singularities determine the asymptotic behavior of the continuous spectrum. Numerical examples illustrate the influence of the proper, real improper, and complex improper modes on the continuous spectrum. The technique avoids the sometimes costly numerical evaluation of the continuous spectral contribution; however, the improper eigenvalues must be found.