Under the pure-bond and the full-slip contact conditions, analytical solutions for hydraulic lined tunnel of non-circular shape are solved by complex variable method, in which the support delay effect of lining and internal water pressure are considered. The stress and displacement solutions on the contact boundaries and lining free boundary of a horseshoe shaped tunnel in orthotropic rock mass are studied under different contact conditions and internal pressures. Contact condition has a significant influence on the tangential stress on lining contact boundary, where the compressive stress on tunnel feet is largest under pure-bond contact condition but smallest under full-slip contact condition. The influence on the asymmetry of mechanical components in lining caused by rock anisotropy and inclined structure plane is more obvious under pure-bond contact condition. Pure-bond contact condition can effectively play the supporting role of lining. Full-slip contact condition reflects the self-bearing capacity of surrounding rock mass. Lining bears the most tension effect caused by water pressure under both two contact conditions.