Abstract: According to the geometrical description of straightness error presented in the national standard GB/T 11336-2004, a new enveloping model of the minimum tolerance zone method for evaluating straightness in a plain and a principle for judging envelop points are proposed in this paper. Based on the principle, a highly efficient algorithm is proposed to search for the envelope points. The proposed algorithm is suitable for searching for the envelope points of a mass points set. A comparison with a traditional method shows that the proposed algorithm had good completeness and produced reliable results. By means of simulation, sets of a million points were calculated using the algorithm and the costs of the algorithm were recorded. The result showed that the time complexity of the algorithm was O(N). The enveloping model proposed in this paper is simple and accurate.