We investigate theoretically the resonant inelastic x-ray scattering (RIXS) at the K edge of Si with systematically varying transfered-momenta, incident-photon energy and incidentphoton polarization. We confirm theoretically the anisotropy of a RIXS and provide a quantitative explanation of a experiment on RIXS at the K edge of Si (Y. Ma et al., Phys. Rev. Lett. 74, 478 (1995)). We clarify the implication of the spectral shape. KEYWORDS: resonant inelastic X-ray scattering, K edge of Si, anisotropy 1