The expansion of a superbubble is investigated both analytically and numerically. Our model implements the thin-layer approximation in a vertical profile of density as given by an isothermal self-gravitating disc. A precise comparison with the results of numerical hydrodynamics is given. Analogies are drawn with the Kompaneets equation that includes the quadratic hyperbolic-secant law in the list of the plane-parallel stratified media. An astrophysical application is made to the superbubble connected with the two worms 46.4+5.5 and 39.7+5.7. The effects of the rotation of the Galaxy on the simulated radius and on the velocity are introduced. The worms with their strong limb brightening visible on astronomical maps are explained in the framework of image theory.