To reveal the creep mechanical properties of sandstone and mudstone fillers under different mix proportions, shear creep tests were conducted on sandstone and mudstone fillers under different mix proportions. The experiment found that the stress-strain curve of the filling material exhibited obvious nonlinear characteristics. Therefore, a viscoelastic modulus reflecting different mix proportions and load times was defined to describe the viscoelastic deformation of the filling material. A unsteady elastic body was established to describe the instantaneous elastic deformation, and an SP element was introduced to construct a unsteady viscoplastic body to characterize the viscoplastic deformation. Thus, a nonlinear creep mechanical model of sandstone and mudstone filling material under different mix proportions was obtained. Simultaneously the new model and the basic model were used to simulate the creep test data of fillers, and verify that the new model is reasonable and feasible. The research conclusions provide a reference for the long-term stability evaluation of wharf sand-mudstone mixed filler foundation.