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Bucket elevators are efficient machines to transport the granular materials in the vertical direction or along the inclined planes. Traditional bucket elevators have strong limitations in the discharging position and discharging mode. So it has important practical significance to design and develop a chain bucket elevator with multipoint discharge which can realize the horizontal and vertical simultaneous continuous transportation. The bucket is the load bearing component of the bucket elevators. This article presents the method of solving the maximum contour of the bucket, which is the combination of analytic method and graphical method. The constraint conditions and the mathematical model of the interference analysis are obtained by the interference analysis at the inflection points, and the boundary contour of the bucket at the inflection points is obtained by solving the constraint equation with MATLAB. And the boundary contour of the bucket at the discharging position is obtained by the graphical method. Therefore, the maximum contour of the bucket is determined, which can ensure not only that there is no interference between the adjacent buckets in the whole process but also that the granular materials can be fully discharged and the maximum loading capacity of the buckets can be achieved.