A boundary integral equation method which utilizes the Green's function for a 2-half-space acoustic medium and the Fourier--Bessel representation of the acoustic field within a cylindrical object is presented. This formulation allows for the accurate computation of the acoustic field scattered from a cylindrical object (possibly, with interior layering) which can be above, below, or intersect the waveguide interface. The waveguide Green's function and its radial derivative are expressed in terms of wave-number integrals. The asymptotic (large wave-number) behavior of these integrals is then evaluated in terms of Hankel functions and asymptotic reflection and transmission coefficients. The numerical treatment of these terms must be considered carefully; in particular, for the case of the partially buried cylinder. Spectral backscattering curves are computed for cylinders with varying degrees of burial. Also, the results of two-dimensional full field computations are shown.