In this paper, we present a matrix-based technique for reconstructing solids with quadric surface from three orthographic views. First, the relationship between a conic and its orthographic projections is developed using matrix theory. We then address the problem of finding the theoretical minimum number of views that are necessary for reconstructing an object with quadric surfaces. Next, we reconstruct the conic edges by finding their matrix representations in space. This effectively constructs a wire-frame model corresponding to the three orthographic views. Finally, volume information is searched within the wire-frame model to form the final solids. The novelty of our algorithm is in the use of the matrix representation of conics to assist in the 3D reconstruction, which increases both the efficiency and the reliability of the proposed approach.