<p>Deep underground rock masses are susceptible to irreversible damage under excavation, resulting in significant deformation and potential instability of engineering structures. Considering the confining-pressure effect, this paper introduces a strain-softening model according to the triaxial compression curves. The evolution of cohesive strength with the plastic index is first established and the dilatancy parameter is developed based on the axial and hoop softening moduli <i>d</i> and <i>m</i> of stress–strain curves. According to the proposed confining pressure-sensitive strain-softening model, the closed-form solution for circular openings is derived. The proposed solution is verified through the comparison with the previous results in elastic–perfectly plastic, elastic–brittle–plastic, and strain-softening rock masses. The stress, displacement, and ground response of a circular tunnel in basalt and marble are analyzed. The influence of <i>d</i>, <i>m,</i> and support stress on cohesive strength and deformation is discussed, revealing that strength degradation during excavation is primarily governed by <i>d</i>, while displacement is more sensitive to <i>m</i>. Optimization guidelines for the design of support stress are provided to maximize the self-bearing capacity of the surrounding rock. The proposed solutions can well predict the plastic zone and distributions of stresses and displacement in the auxiliary tunnel in the Jinping II Project, providing a reliable theoretical foundation for engineering design and construction.</p>