Purpose This paper aims to model a three-dimensional twisted geometry of a twisted pair studied in an electrostatic approximation using only two-dimensional (2D) finite elements. Design/methodology/approach The proposed method is based on the reformulation of the weak formulation of the electrostatics problem to deal with twisted geometries only in 2D. Findings The method is based on a change of coordinates and enables a faster computational time as well as a high accuracy. Originality/value The effectiveness of the adopted approach is demonstrated by studying different configurations related to the IEC 60851-5 standard defined for the measurement of the electrical properties of the insulation of the winding wires used in electrical machines.