The inverse scattering of buried inhomogeneous uniaxial dielectric cylinders is investigated. Dielectric cylinders of unknown permittivities are buried on a half-space and illuminated by a group of unrelated waves incident from another half space where the scattered field is recorded. By proper arrangement of various unrelated incident fields, the difficulties of ill-posedness and nonlinearity are circumvented, and the permittivity distribution can be reconstructed through simple matrix operations. The algorithm is based on the moment method and the unrelated illumination method. Numerical results are given to demonstrate the capability of the inverse algorithm. Good reconstruction is obtained even in the presence of additive random noise in measured data. In addition, the effect of noise on the reconstruction result is also investigated.