Determination of cross-sectional area of glass and carbon fibres is a critical part of mechanical testing of the fibres. The present study focuses on the vibroscope method which is based on frequency measurements of a fibre under tension. Three data analysis procedures, named simple, direct and iterative, are presented, providing estimates of the fibre cross-sectional area with increasing accuracy. The simple procedure underestimates the cross-sectional area with about 0.4 – 2.0 % and 0.4 – 3.7 % for the tested glass fibres and carbon fibres, respectively. The cross-sectional area determined by the direct procedure deviates only marginally from the most accurate cross-sectional area as determined by the iterative procedure. Histograms of cross-sectional areas of glass and carbon fibres are presented to show the large variation of cross-sectional areas between individual fibres. Stress–strain curves of the tensile tested fibres are presented, and the small variation of stress–strain curves between individual fibres contributes to the validation of the vibroscope method.