An ab initio-constant pressure technique is applied to study the pressure-induced phase transition of germanium under uniaxial and hydrostatic stresses. The method successfully reproduces a first order phase transition from the diamond structure to a beta-Sn structure with the application of hydrostatic pressure. The simulations reveal that the uniaxially compressed germanium also undergoes similar phase transition via an intermediate state having a space group of I4(1)/amd. The transition pressure is significantly lowered for the uniaxial case, and the physical origin of which is associated with bond bending. The computed Poisson ratio of germanium agrees with experiments.