This paper presents the integration of Finite Element (FE) techniques with B-rep solid modeling. Algorithms for constructing B-rep solid models from a finite element meshes are presented. The finite element mesh data, which consists of node coordinates and connectivity information, is read in from any standard finite element analysis package (currently SDRC IDEAS and MSC/XL) and then processed to construct a polyhedral non-manifold B-rep solid model of the geometry. Since the finite element mesh of a solid object is essentially a non-manifold object, existing geometric modeling data structures based on two-manifold topologies cannot represent it directly. In this work the non-manifold radial-edge data structure is used for the internal representation of the finite element mesh. The mesh is then processed using non-manifold topology operators to eliminate internal nodes and elements to arrive at the solid model that is a polyhedral boundary representation. The results are useful for design automation through the integration of CAD with finite element analysis, shape optimization, as well as the manufacturing of geometry stored as a finite element mesh.