An efficient algorithm for reconstructing all polyhedral 3D objects from two orthographic views is presented. Since the two-view orthographic representation of a 3D object is ambiguous, it requires a numerous amount of combinatorial searches in the process of reconstruction. Also, multiple number of solutions in contrast to the designers intention can be existed in the problem. This paper proposes a two phase algorithm to reduce the search space and to select the most plausible solution described by the given projections. First, the partially constructed objects are reconstructed from the restricted candidate faces corresponding to each area on the two-view drawings in its first phase. Then the complete objects are obtained from the partially constructed objects by adding other candidates with geometrical validity in the second phase. The algorithm performs a combinatorial search based on the face decision rules along with two heuristics. Decision rules check geometrical validity and heuristic rules enhance the search speed. In addition, the reconstruction finds the most plausible 3D object that human observers are most likely to select first among the given multiple solutions. Several examples from a working implementation are given to show the completeness of the algorithm.