A process for joining variously shaped vacuum heat insulating elements having edges adapted to be butted against each other or to overlap each other. A bellows is tightly connected with each vacuum heat insulating element in the area of its edges, the free edge of the bellows projecting beyond the element. The heat insulating elements are positioned such that the edges of the bellows rest against one another in an aligned manner or overlap, and the bellows are tightly connected with one another. The heat insulating elements are then moved against one another until their edges rest against one another or overlap, and are tightly connected with one another. The gap at the joint formed between the heat insulating elements and the bellows is evacuated and closed off tightly.