Modeling of time shifts associated with time-lapse (4D) seismic surveys is helpful in evaluating reservoir depressurization and inverting for subsurface stress. Using coupled geomechanical and full-waveform seismic modeling, we study the influence of compaction-induced stress and strain around a simplified reservoir on compressional (P), shear (S), and mode-converted (PS) waves. We estimate compaction-induced time shifts and analyze their dependence on reflector depth and pressure drop inside the reservoir. Time shifts between synthetic baseline and monitor surveys are obtained by processing techniques that are potentially applicable to field data. Although P-wave time-shift lags for reflectors in the overburden are indicative of induced anisotropy, they are two to three times smaller than S-wave time-shift leads for reflectors beneath the reservoir. We also investigate the contributions of the deviatoric and volumetric stains to the time shifts for all three modes. Time shifts for Sand PS-waves are strongly influenced by elevated volumetric and deviatoric strains inside the reservoir. Almost constant S-wave time shifts for a range of offsets and source locations indicate that the contribution of stress-induced velocity anisotropy to shear-wave signatures is weak because the symmetry is close to elliptical. Our modeling also shows that mild tilt of a rectangular reservoir, or its replacement with an elliptically shaped reservoir of the same aspect ratio, has little influence on time shifts. Potentially, the developed methodology can be applied to estimate compaction-induced stress fields using simple compartmentalized reservoir models.