In this paper an efficient coupled-mode method is presented for modeli
ng acoustic propagation in a multi-faceted oceanic waveguide. The meth
od is based on the concept of ''wedge modes,'' which are identical to
the usual normal modes of a range-invariant waveguide except that the
mode functions are referenced to the are of a circle rather than a ver
tical line. Within each wedge-like section of the waveguide, wedge mod
es are assumed to propagate adiabatically. At junctures of waveguide f
acets, the incident field from the previous wedge is coupled into the
wedge modes of the following wedge, and the new set of wedge modes is
again propagated adiabatically. ''Leaky modes,'' which account for ene
rgy that is only partially reflected at the basement interface and whi
ch are important only at shea ranges in flat waveguides, are included
because conversion between leaky and trapped modes is important in man
y range-variable waveguide geometries. Coupling of the two sets of wed
ge modes at facet interfaces is performed using a method that does not
assume mode orthogonality in the water. Agreement in the field comput
ed using the coupled wedge mode method and a parabolic equation method
is found to be very good.