Tight conglomerate rocks consist of gravels and rock matrices. The existence of these stiff gravels leads to heterogeneity in conglomerates and makes it difficult to characterize rock mechanical properties, which then affects drilling and hydraulic fracturing operations in tight conglomerate hydrocarbon-bearing reservoirs. This case study introduces a series of experimental and numerical analyses for the better understanding of rock deformation and elastic wave propagation patterns in a tight conglomerate reservoir in Junggar Basin, China. Tri-axial compression tests, acoustic test, and finite element modeling of rock deformation and elastic wave propagation in conglomerate rocks are presented. Experimentally tested samples exhibit good brittleness and shearing failure patterns, while well correlated static-dynamic elastic moduli and P-S wave velocities are captured. Numerical results show that the existence of stiff gravels leads to strong direction-dependent stress and strain anisotropies. Stress concentrations are also induced by gravels radially and axially. In the elastic wave domain, stiff gravels facilitate the propagation of elastic waves. The gravel close to the wave source also induces stronger compressive/tensile states in the wave domain, indicating that the existence of gravels in conglomerates can alter waveforms. This integrated approach improves the quantitative understanding of stress, strain, and elastic wave responses in heterogeneous tight conglomerates. This case study also serves as a reference for the brittleness evaluation and geomechanical evaluation in the study area. The contribution of this work is primarily about the integrated experimental study, solid deformation modeling, and elastic wave modeling of tight conglomerate rocks.