The technological process of the production of a jacquard ribbon on a weaving machine using the mathematical method of rotatable planning of a second-order experiment has been investigated. The geometric interpretation of the mathematical model is studied using slices. The optimal technological parameters of the jacquard ribbon production have been determined. The level of breakage of the warp yarns is 0.05 breaks per 1 m of fabric with the filling tension of the warp -20 cN, the size of the overlap -15 mm. and the position of the rock is 25 mm above the breast.