This thesis explains problems that occur in piano tuning process due to the non-negligible bending stiffness of piano strings. Normally, a piano technician adjusts tensions of the strings such that the ratios between their fundamental frequencies follow a certain harmonic pattern. In consonant intervals it is aspired towards the absence of acoustic beats, which are perceived as slow periodic variations in volume that occur due to the interference of two tones with slightly different frequencies. Typical mathematical models of an ideal string (without bending stiffness) under axial tension predict the second natural frequency to be twice the first, the third three times the first, and so on. However, piano wires under realistic conditions have the second natural frequency slightly higher than twice the first natural frequency. As a result, the musical scale during the piano tuning process becomes stretched. This is because a piano technician adjusts the tension of the string so that the second natural frequency of its octave lower counterpart matches the first natural frequency of the string currently tuned, trying to eliminate acoustic beats. In this thesis the causes of the stretching effect are explained using a mathematical model to calculate natural frequencies of a beam under constant axial tension. The results obtained using the model of a tensioned beam are compared to the results obtained using the model of an ideal string without bending stiffness, and those results are compared to measured fundamental natural frequencies of tones on a real piano. In the example of a pinned-pinned beam it is shown that the second natural frequency is not equal to twice the fundamental natural frequency, but slightly higher. It is shown that with the increase of the tensile force, the higher natural frequencies of a tensioned beam tend to the natural frequencies of a tensioned string. However, with a finite axial load that is not the case so that the stretching effect cannot be easily avoided.