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The technology of combining a negative Poisson's ratio (NPR) anchor cable with a double-layer truss support technology (N-DTST) is a new support technology for deeply buried tunnels. To evaluate the stability of the surrounding rock support after the application of this new support technology in the Sichuan–Tibet Railway tunnels, geomechanical model tests were conducted for the first time. A model test loading system with intelligent numerical control and automated analysis was developed to reveal the changing patterns of displacement and stress in the surrounding rock of tunnels. The test results revealed the following: (1) After the burial depth exceeds 800 m, the tunnel undergoes large deformations with displacements greater than 37.5 mm, and the traditional anchor cable support fails; (2) In the burial depth range of 800–2,000 m, the new support technology can control the surrounding rock deformation, and the surrounding rock displacement is less than 10 mm; (3) After the tunnel excavation, the radial stress decreases and the tangential stress concentrates. When the burial depth is greater than 800 m, the radial stress compensation provided by the anchor cable no longer meets the stability of the tunnel surrounding rock, and the new support technology can provide high stress to support the deeply buried tunnel; (4) After the burial depth exceeds 2,000 m, butterfly-shaped damage occurs on the tunnel surface, the truss structure inside the tunnel is damaged, and the support structure fails, so it is recommended to carry out reinforcement support at the arch shoulder. The research results verify the effectiveness of the new support technology and provide an important reference for the support of the surrounding rock in deeply buried tunnels. Practical Applications: Common Poisson's ratio anchors/ropes or shotcrete are widely used in tunnels as the core support structure. They often fail to meet the requirements of fractured rock, expansive rock, and high-ground-stress soft rock tunnels because they cannot adapt to the large deformation characteristics of the catastrophic rock mass. Based on this, this paper proposed a new support technology: an anchor rod/rope with a negative Poisson's ratio material combined with a double-layer three-dimensional truss for joint support of the tunnel. To verify the feasibility of this technology, the research and development team developed a new design for the structure. To verify the feasibility of this technology, a large-scale geomechanical model test system was developed, and a comparative model test was conducted using this test system in combination with the ground stress environment of the Sichuan–Tibet Railway to verify the effectiveness of the new support technology proposed in this paper, which provides a reference for the world's deep buried tunnel support technology. [ABSTRACT FROM AUTHOR]