The coupled wave equations for frequency doubling of Gaussian beam propagating in birefringent uniaxial anisotropic medium are given. Based on them, specific physical models of single and twin crystal of barium metaborate (BBO) material have been established, and numerically computed results show the distribution of harmonic power flow, the electric field temporal distribution of harmonic at probe point on exit surface of the crystal, the output total energy, the output spectra of light and also the input angular spectra of beam. We make detailed analysis of various influences mainly from beam waist, medium structure and properties of material on second harmonic generation and give some reasonable explanations. The research results will benifit the study on nonlinear optical properties of uniaxial medium and optical crystal devices.