Disclosed a thermal- and sound-insulating container having a chamber, which is defined by multilayer wall structure including vacuum layers therein. The chamber is made as small as possible the surface area thereof to achieve the high insulating effectiveness. The thermal- and sound-insulating container is comprised of the multilayer wall structure with vacuum layers therein, which constitutes the chamber defined in a hollow cylinder partially having a flat secant face, the hollow cylinder having a cross section of a circle or an ellipse that closely resembles the circle. The multilayer wall structure is composed of a pair of confronting frames arranged spaced away from each other, surface panels attached to the frames to define an empty space between the confronting frames, and sealing members arranged between the frames and the peripheries of the surface panels so as to keep the space at vacuum. The thermal- and sound-insulating container may further include honeycomb cores arranged in the vacuum space, resin-made films enclosing hermetically the surface panels, and vacuum-failure indicators for detecting the rupture caused in the resin-made films of the surface panels.