The present disclosure relates to an insulated container construction and describes more specifically an embodiment of such construction which is in the nature of a disposable hot drink cup which includes an outer member shaped generally as a frustum of a cone having an open upper end and a closed bottom end and constructed of a paper material which preferably has a thickness in the range of from about 0.305 mm. to 0.457 mm. The container construction, also, includes an inner member shaped generally as a frustum of a cone and having an open upper end and a closed bottom end and residing within the above referred to outer member. The inner member is constructed of a synthetic resin or plastic material and preferably polystyrene and preferably of a thickness in the range of from about 0.127 mm. to 0.381 mm. The open upper end of the plastic inner member is turned outwardly and back upon itself to form a lip portion which engages the lips of a user of the cup and keeps the lips of the user of the cup away from the upper edge of the paper construction of the outer member. Wall means are provided on one or both of the outer and inner members to define an insulating air space between the two members to give the container construction a high insulation value. With this particular structure the paper outer member provides the primary support structure and the plastic inner member serves the primary function of holding the liquid which is to be carried by the container. Since the liquid is carried by the plastic inner member, it is not necessary to leakproof the paper material of the outer member. The wall means which define the insulating air space form preferably a triangular-appearing shape in cross section as viewed in an axial direction of the container.