The temperature and density fields associated with the motion of an ideal gas acted on by an expanding piston have singularities at the piston surface [1–3]. These arise through nonallowance for heat conduction by the gas, which plays the determining role near the surface of the piston. We shall solve the problem of motion of a heat-conducting gas acted on by an expanding heat-insulated piston by the method of interior and exterior expansions. To this end we construct the principal term of the interior asymptotic expansion by splicing it with the solution for an ideal gas which constitutes the principal term of the exterior asymptotic expansion. This yields a solution free from singularities. A similar solution for the strong-detonation problem was obtained by Sychev [4].