The reconstruction of a solid from its contour definition is, basically, a conversion from boundary to volume representation, and it has been addressed in the literature in several instances. The simultaneous reconstruction of several solids— in any number and in any nesting order—from a set of contours is a more complex problem, for which a solution is presented. The latter consists of three parts: the separation of connected contours, the filling of those contours which indeed contain a volume, and the leaving of the other components as dangling elements. The general case is considered in which all the contours are given as one set of voxels; this means that contiguous contour elements may not be associated with the same object. Together with the reconstruction of all multishell solids, their inner structure is identified in the sense that it is determined whether a solid is inside another, and, if so, at which level of nesting. This information is condensed in a graph structure called the region-containment tree. The methodology used relies on union-finding techniques coupled with tree traversals in an octree environment. Various approaches to tree traversals and the propagation of adjacency information are explored. The method with the best runtime uses an initial search to identify each contour. This is followed by connectivity labelling (in the active border version) to separate and fill each solid component. Testing has been carried out in seven cases. In five of these, an independent solid modeller is used as a reference, and in two, a different surface-to-solid conversion is used.