Interference detection between surfaces of the part and the cutting tool is important in 5-axis tool path planning process. The purpose is to ensure the tool in an interference-free posture. There are many ways to detect interference; in this article, the subdivision method is applied. In this research, a simple but high efficiency algorithm based on triangle subdivision has been developed to deal with the two spatial triangles interference detection problems. In the proposed algorithm, only the three vertex coordinates of the two spatial triangles are given. The equation of the plane on which the triangle set lies is then generated, respectively. The intersection line equation can be obtained by combining the two equations. Because of the computer truncation error, errors must have been brought into the obtained line equation. A special method, which is not sensible with the errors of the line equations, is developed to determine whether the intersection line intersects with either of the two triangles. If both are yes, then the intersection points are calculated to further determine whether the two triangles interference by setting a faraway point on the intersection line. The algorithm is efficiency as it concerns only with the solution of two plane equations; and once the none-interference condition satisfies, the algorithm could break from any step.© (2010) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.