Abstract: A method for reconstructing solids with quadric surface from orthographic views is presented. First, the wire-frame model corresponding to the three orthographic views is constructed. In order to generate 3D conic edges in the wire-frame model, a five-point method is firstly utilized to obtain the algebraic representations of all 2D-projection curves in each view, and then all algebraic forms are converted to the corresponding geometric forms analytically. The locus of a 3D conic edge can be derived from the geometric forms of the relevant conic curves in three views, and the relationship between a 3D conic and its orthographic projections is established. In addition, the support plane of each 3D conic edge is created. Finally, all possible faces are searched within the wire-frame model, and all true faces are found to assemble the final solids according to the properties of 2-manifolds, Moebius rule and the characteristics of orthographic projections. The method extends the range of objects to be reconstructed and imposes no restriction on the axis of the quadric surface.