<p>Tunnel cavities are often excavated in layered rock mass characterized by the pronounced cross-anisotropic behavior. To simulate these kinds of problems, a new cross-anisotropic constitutive model is developed to represent both the stiffness and strength anisotropy of layered rock mass, with the aid of a cross-anisotropic elastic compliance matrix and a proposed generalized anisotropic stress tensor, respectively. By formulating the constitutive model in second-order cone programming (SOCP) format, the SOCP optimized finite element method (FEM-SOCP) is established and applied to tunnel cavity analysis involving cross-anisotropic rock mass. The proposed generalized anisotropic stress tensor with three stress scaling factors endows the FEM-SOCP framework with promising feasibility, flexibility and practical applicability in simulating the cross-anisotropic rock mass. By introducing five independent elastic constants into the cross-anisotropic elastic compliance matrix, the bedding plane spacing can be taken into account in cross-anisotropic rock mass. Based on the analyses of three examples, namely an unsupported tunnel, a cylindrical cavity expansion and a tunnel in layered rock mass, it is found that the implicitly modeling FEM-SOCP can capture the deformation behavior and failure mode of cross-anisotropic rock mass induced by tunnel cavity, being consistent with those simulated by the explicitly modeling discrete element method (DEM).</p>