With the widespread application of large- quasi-rectangular pipe-jacking tunnels in urban road traffic engineering in China, higher requirements have been put forward to control the influence of their construction on the surrounding environment. To scientifically evaluate the stability of large- quasi-rectangular pipe-jacking tunnels under-passing existing box culverts, we proposed a novel viscoelastic-plastic model coupling Biot consolidation with non-stationary parameter shear creep (NPSCBCVPM) to fully characterize the coupling effect of consolidation and rheology of saturated soft soil. NPSCCBVPM was developed in Fortran as an ABAQUS user material subroutine. In addition, the NPSCBCVPM was compared with the creep tests of undisturbed soft soil and the generalized Nishihara creep model (GNCM). Finally, the proposed model was applied to the large- quasi-rectangular pipe-jacking tunnel under-passing existing box culverts of Songhu Road in Shanghai. The results show that NPSCBCVPM are in good agreement with the creep tests of soft soil, and NPSCBCVPM can better reflect the nonlinear rheological characteristics of soft soil than GNCM. Furthermore, the proposed model can scientifically evaluate the viscoelastic-plastic stability analysis of large- quasi-rectangular pipe-jacking tunnel under-passing box culvert. Further research should focus on developing three-dimensional NPSCBCVPM to better evaluate the spatial response of the box culvert structure and surrounding soil to the entire construction process of large- quasi-rectangular pipe-jacking tunnels.