Abstract <p>Many rocks exhibit viscoelastic behavior to varying degrees. In practice, viscoelasticity can lead to various effects. Among the most significant are the effects of narrowing of wells during drilling at the stages before the casing is lowered and cemented in. Rocks such as clays or argillites, often found in oil or gas field caprocks, are viscoelastic, as has been shown in many experimental studies. This article provides an example of such an experiment. To describe the effect of changing well geometry over time, the Burgers model was chosen, which is a combination of the Maxwell and Kelvin models. Using the operator method, solutions were obtained for the stress–strain state of the near-well zone under the assumption of the absence of volume viscoelasticity. It is shown that the solution makes it possible to estimate the shape and time of safe deformation of the well when setting the maximum permissible minimum radius of the well.</p>