The Wave-Envelope (WE) method has been used in acoustic and electromag
netic wave problems to model the circular unbounded domain surrounding
a source. Here a new formulation is used to apply the WE method to el
ectromagnetic wave problems in which the outer boundary is not circula
r, bur may be elliptical or rectangular. Results for both radiation an
d scattering problems confirm that the new boundary shapes provide sub
stantially the same accuracy as the circular boundary.