An algorithm for the computation and representation of van der Waals surfaces and volumes of supermolecules (several overlapping molecules) by a set of grid points originating from an equidistant lattice is described in detail. The grid points in this set belong either to the "outer" surface of the van der Waals body or to a layer just below that outer surface. By means of this double layer (outer and inner) it is possible to represent the volume via the surface without referring to grid points lying inside the body. The algorithm is based on the octree concept, which means that the final relevant lattice points are derived by the successive refinement of an initial coarse lattice. The main features of the algorithm are the automatic elimination of inner atoms irrelevant for the surface definition and the association of any surface point with only those atoms which define the surface in the vicinity of these points. The most remarkable consequence of these features is that the amount of computation is almost independent of the number of atoms in the supermolecule. The algorithm can be used in solving problems arising in drug design, protein folding, molecular graphics, etc.