Prototypes of a design are always needed for the purpose of visualization and evaluation in the aspect of manufacturability functionality, and aesthetic appearance. Since the prototyping process requires a significant amount of cost and time, various rapid prototyping processes are recently being introduced in the process. However, it is usually necessary for a part built up by a rapid prototyping system to be refined by a post-processing process, in which the stair steps on the surfaces, the support structures (if they exist), and the unprocessed material are eliminated. This post-processing is usually done manually and is a time-consuming task. Especially, eliminating the trapped volumes, the volume of the unprocessed material entrapped by the solidified portion, is sometimes impossible in some processes. This study provides a designer with a tool to detect the existence and to calculate the quantity of the trapped volumes at the given build-up direction, so that the proper build-up direction is chosen or the part is built by pieces to avoid the problems caused by the trapped volumes in advance. Since the proposed algorithm can efficiently calculate the amount of the trapped volumes at any build-up direction, it has the potential of such application as optimizing the build-up direction to minimize the trapped volumes.