Based on a previously proposed thermodynamic analysis, we study the relative stabilities of five Si phases under uniaxial compression using ab initio methods. The five phases are diamond, beta-tin, sh, sc, and hcp structures. The possible phase-transition patterns were investigated by considering the phase transitions between any two chosen phases of the five phases. By analyzing the different conributions to the relative pahse stability, we identified the most important factors in reducing the phase-transition pressures at uniaxial compression. We also show that it is possible to have phase transitions occur only when the phases are under uniaxial compression, in spite of no phase transition when under hydrostatic commpression. Taking all five phases into consideration, the phase diagram at uniaxial compression was constructed for pressures under 20 GPa. The stable phases were found to be diamond, beta-tin and sh structures, i.e. the same as those when under hydrostatic condition. According to the phase diagram, direct phase transition from the diamond to the sh phase is possible if the applied uniaxial pressures, on increasing, satisfy the condition of Px>Pz. Simiilarly, the sh-to-beta-tin transition on increeasing pressures is also possible if the applied uniaxial pressures are varied from the condition of Px>Pz, on which the phase of sh is stable, to that of Px