In this paper, the resonant characteristics of the rectangular microstrip patch antenna on uniaxially anisotropic substrates are determined via spectral domain analysis. The anisotropic substrates are characterized by both permittivity and permeability tensors. Green's functions of the structure in Fourier transform domain are determined using the Galerkin's technique. The sinusoidal functions are selected as the basis function, which show fast numerical convergence. Numerical results concerning the effects of electric anisotropy and antenna parameters on the resonant characteristics of rectangular microstrip antenna are presented and discussed. Results are compared with previously published data and are found to be in good agreement.