Purpose: The paper presents an analysis of the influence of design features of the flexspline in a harmonic drive, such as the relative radial deformation, the relative coating thickness and the design features of the basic rack tooth profile, on stress values in the bottom lands of a toothed ring. Design/methodology/approach: In numerical calculations, the software developed at the Faculty of Transport of the Silesian University of Technology was used. The program automatically generates a profile of the flexspline and a boundary elements mesh on the grounds of the flexspline and working tool assigned parameters. In the analysis of the state of stress, the boundary element method (BEM) was applied. Findings: A decreased value of the curve radius of the head of the basic rack tooth profile results in a change in the width of the tooth bottom land, shortening of the transition curve in the tooth base and a reduction of the tooth thickness at its base, which in turn leads to increased values of stress. Yet, the influence of the relative curve radius of the head of the basic rack tooth profile on the stress value is insignificant. The increase of the torque and relative coating thickness for different value of the curve radius of the head of the basic rack tooth profile cause an increase of stress in the bottom lands of the toothed ring. Research limitations/implications: The paper presents strength calculations for the teeth in toothed ring of a flexspline of a double harmonic drive by means of boundary elements method (BEM). The results of numerical calculations correspond in terms of their quality to the results presented in the literature, which were calculated by finite element method (FEM). Originality/value: In the analysis of the state of stress of toothed ring of flexspline, the boundary element method (BEM) was applied.