Compared to indirect bandgap Ge semiconductors, carrier radiative recombination efficiencies of pseudo-direct bandgap Ge semiconductors (PD-Ge) with low-intensity tensile strain and direct bandgap Ge1–xSnx alloy (D-Ge1–xSnx) with high Sn component are high. Since the carrier mobility of PD-Ge and D-Ge1–xSnx is high, they can be applied to high-speed and high-performance electronic devices. As a result, PD-Ge and D-Ge1–xSnx have potential for monolithic optoelectronic integration chips (MOEIC). The energy bandgap of work area which in LED, waveguide and detector of MOEIC should meet relationship Eg,waveguide > Eg,LED > Eg,detector. To achieve MOEIC, the band structures of PD-Ge and D-Ge1–xSnx need to be modulated. The band structures can be modulated by applying uniaxial stress using SiN film, and the process is compatible with MOEIC. In this paper, based on kp band theory combining with deformation potential, energy bandgap models of PD-Ge and D-Ge1–xSnx under uniaxial stress are studied, and then change rules are proposed. It aims to provide important theoretical reference for design and implementation of Ge-based MOEIC.