The propagation of flattened-Gaussian beams(FGBs) in uniaxial crystals is studied based on the paraxial vector theory of the propagation of beams in uniaxially anisotropic media. Analytical propagation equations are derived, which permit us to study the propagation properties of FGBs in unaixal crystals in a simple way. It is shown that the initial circular symmetry of FGBs cannot be kept up, and the state of polarization of FGBs varies during propagation due to the anisotropy of crystals. The spatial evolutions of ordinary and extraordinary components, as well as these in x and y directions in the crystals originating from input FG Bs are illustrated with detailed numerical examples.