  The Rayleigh conjecture on the representation of the scattered field in the
exterior of an obstacle $D$ is widely used in applications. However this
conjecture is false for some obstacles. AGR introduced the Modified Rayleigh
Conjecture (MRC), and in this paper we present successful numerical algorithms
based on the MRC for various 2D and 3D obstacle scattering problems. The 3D
obstacles include a cube and an ellipsoid. The MRC method is easy to implement
for both simple and complex geometries. It is shown to be a viable alternative
for other obstacle scattering methods.
