The differential cross sections for an ellipsoid and elliptic cylinders having Gaussian electron-density distributions have been obtained by a ray-tracing procedure. Calculations for the case of an external magnetic field were restricted to the ellipsoidal distribution. The results show that the scattering is extremely sensitive to the orientation of the body. A peak in cross section occurs at the scattering angle corresponding to the ray normal to the critical surface, and increases as the surface becomes flatter. The cross section is sensitive to the ratio of peak density to critical density for moderate values but becomes relatively insensitive when the ratio exceeds 3. The total cross section (shown only for the elliptic cylinder) is a very sensitive function of both orientation and ratio of major to minor axes. The introduction of a magnetic field decreases the ordinary ray cross section; the extraordinary ray exhibits higher cross-sectional values than the nonmagnetic field case. Comparison of the Gaussian ellipsoid with the corresponding conducting ellipsoid shows that the Gaussian has a larger cross section in the forward region but considerably lower values in the back-scatter region.