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Three-dimensional (3D) elastic phononic topological insulator, featuring two-dimensional (2D) surface states, which support the high-efficient and robust elastic wave propagation without backscattering in all spatial dimensions, remains a challenge due to the nature of multiple polarized elastic modes and their complex hybridization in 3D. Here, a 3D elastic phononic topological insulator is designed and observed experimentally by emulating the quantum valley Hall effects. The spatial inversion of adjacent atoms gives rise to a valley topological phase to an insulating regime with complete 3D topological phononic bandgap. The 2D surface states protected by valley topology are unveiled numerically, which are confirmed experimentally to have a great robustness against the straight channel and sharp bends. Further engineering the elastic valley layer with appropriate interlayer coupling, we also demonstrate that layer pseudospin can be created in 3D elastic system which leads to 2D topological layer-dependent surface states and layer-selective transport. Our work will be a key step for the manipulation of elastic wave in 2D topological plane and the applications of 3D elastic topological-insulator-based devices with layer-selective functionality.