This work indicates that the prediction of the geometric indicators of the quality of the machined surface in the design of technological operations for milling a profile surface of work-pieces with low rigidity is possible, on the basis of an analysis of the elastic displacements of the technological system elements, the flexural rigidity of the work-piece as a function of its initial dimensions, the locating chart and the physical and mechanical characteristics of the material being processed. The article describes the characteristics of the elements of the technological system for the profile milling of work-pieces of low rigidity; The analytical dependencies linking the elastic displacements of the work-piece during the processing of various wood species with elements of the milling mode and the design parameters of the mill are given. Extreme total elastic displacements of the technological system during the cutting process are determined. Mathematical models of the maximum geometric error of the machined surface, as a function of the work-piece's flexural rigidity and the spindle unit, are established. Based on the results of the analysis, recommendations for improving the accuracy of the product were developed.