Triangle's checking in 3D faceted models is an essential step in gouging detection and elimination process. To check whether model surface intersects the tool, every triangle in the model has to be checked. Unfortunately, this process takes much time. Since the computer can't see and doesn't know which triangles located under the current tool position, then the triangles all over the surface model should be checked. To reduce the time, region checking at every position of tool has to be detected. Triangles that have to be checked are only in that region. The way of creating the region can be done by bucketing. Bucketing process will make some buckets as representation of regions and each bucket will be filled with triangles that lie in the corresponding region. There are several bucketing methods. This paper will explain all methods which have been implemented in the research.