Tunnel excavation causes ground movements which have the potential to cause damage to other buried infrastructure, including pipelines. This note examines the tunnel–pipeline interaction problem from the context of an elastic-continuum based approach. A theoretical proof is provided which shows that there is a constraint of volume loss equality between the greenfield displacement input and the resulting deformed pipeline shape. In addition, for an assumed Gaussian curve fit for the input greenfield displacements, it is shown that the deformed pipeline also fits well to a Gaussian shape. These two features are used to develop simple expressions for the prediction of pipeline bending moments. An interesting outcome of the analysis, whereby displacement and bending moment ratios can be related using a simple power law expression, is demonstrated and shown to agree well with experimental data.