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An elastic continuum solution and a Winkler solution of the problem of tunnelling effects on existing pipelines are given. A comparison is made between an elastic continuum solution and a closed-form Winkler solution with Vesic subgrade modulus. Although applying the Vesic expression results in the same moments and displacements under external loading in a Winkler system and the elastic continuum, it is found that its use is not necessarily adequate for the problem of tunnelling effects on pipelines and may not be conservative owing to possible underestimation of bending moments. An alternative expression for the subgrade modulus is provided, resulting in similar maximum bending moments in the Winkler and elastic continuum systems.