Abstract An analytical solution has been developed for calculation of elastic stresses occurring around tunnels or galleries with conventional shapes which are frequently used in mining and civil engineering. Basically, the cross sections considered in the solution have one vertical axis of symmetry, and the roof is arched while the floor may be flat or parabolic. The solution is obtained by using the conformal mapping technique of the complex variable method. After a brief explanation of the method, explicit formulation is presented, and equations for the induced stresses are given. Using the solution, distribution of stresses around the tunnels is determined for various in situ stress conditions. Finally, potential applications of the solution are demonstrated by examples in rock engineering.