||Nowadays, most designers still prefer to express their creative design idea through 2D sketches. Current geometric modeling systems do not provide 3D freeform modeling tools in this manner. In this thesis, the techniques of 3D freeform object modeling using 2D sketches were developed. Abstractions are frequently used along with the models for physical objects. This leads to the non-manifold geometric modeling. Thus, first of all, a non-manifold data structure is defined in this thesis. The presented data structure combines the B-rep and the complex-based representation. Along with the data structure, a set of topological operators is defined to manipulate the entities in the current data structure. Based on the non-manifold data structure and topological operators, this research develops methods to construct and modify 3D freeform objects through 2D sketched input. The construction method is feature based - every reference model has pre- defined features, and the constructed surfaces are related to the features on the reference models. Therefore, the surfaces on models derived from the same reference model can be regenerated automatically with the same features. After a 3D model is constructed, it could be modified by 2D strokes using a number of pre-defined intuitive and efficient operations. These modification operations are painting, cutting, extrusion, smoothing, deformation, and folding. The modification operations are based on a set of re-meshing algorithms, which include a new mesh optimization algorithm that does not make reference to parametric surfaces or point clouds. Since computer-aided design and manufacturing are tightly integrated, an energy based surface flattening method is also included in this thesis. The surface flattening procedure consists of two steps: triangles flattening and planar mesh deformation; and an additional option is introduced to suggest a cutting line on the surface based on the surface energy. Finally, in order to demonstrate the techniques developed by this research, a sketch-based 3D apparel product development platform - GarSketch3D is presented.