The impulse response method is often used to measure firmness of spherical fruits. In this method the fruit is excited using an impact hammer and the response signal is captured using a microphone. This vibration response signal is subsequently analysed and related to the firmness of the fruit. In our work the effect of the shape of pears on their resonant frequencies is investigated using finite element (FE) modal analysis. Fifty differently shaped 3D FE meshes of ‘Conference’ pears were generated using a geometrical modelling system. The FE model was validated, and found to be sufficiently accurate. The length/maximal diameter ( L/ D) ratio and the Fourier descriptors were used as shape descriptors. A strong linear relationship ( r 2>0.84) was found between the third normalised Fourier descriptor (F3) and the resonant frequencies. A weak linear relation was detected using the L/ D and the other normalised Fourier descriptors. A simulation of firmness measurements based on the calculated resonant frequency values was carried out to estimate the Young's ( E) modulus of the pear as a measure of its firmness. The estimated error with these simulations was found to be 31.44, 8.02 and 3.82% if the bending, the compression and the oblate–prolate modes were measured and the L/ D was used as a shape descriptor. If F3 was used, the following error values were found: 6.0% for the bending, 3.39% for compression and 3.38% for the oblate–prolate modes. The results of this study may help in the development of a non-destructive firmness sensor for non-spherical fruits.