  We study Anderson localization of a scalar wave in an ensemble of resonant
point scatterers embedded in an anisotropic background medium. For uniaxial
anisotropy of moderate strength, the mobility edges and the critical exponent
of the localization transition are found to be unaffected by the anisotropy
provided that the determinant of the anisotropy tensor is kept equal to one
upon introducing the anisotropy. Localized modes have anisotropic spatial
shapes although their anisotropy is weaker than the one expected from purely
geometric considerations. The modes with the longest lifetimes are found to be
the most anisotropic and their anisotropy increases with the size of the
disordered medium.
