The underwater tunnels can be regarded as shallow tunnels. So the classical problem of an elastic half plane with a circular cavity

loaded arbitrarily on the horizontal boundary can be used to analyse the stress and displacement fields of the surrounding rock for underwater tunnels. As is known to all

it is much more difficult to deal with shallow tunnels than deep tunnels via the analytical way. Using Verruijt’s conformal mapping function

the region of exclusion of a hole in a half plane is tansfered into a cirque. Then the analytic functions can be expanded as Laurent series in this region. The stress and displacement can be solved by the function of complex varibles method founded by Muskhelishvili. The corresponding calculation program is coded by Fortran. As an example

a specific underwater tunnel is analysed by the Fortran calculation program eventually.