Comparison of Magness-Taylor’s method (MT) with the quasi non-destructive, mechanical method of Fekete (F) and the measurement method for the modulus of elasticity using Instron texture press (EI) was carried out on the fruit of four apple and two pear cultivars. To get a broad range of firmness, fruit were stored under normal atmosphere, CA and ULO conditions for various periods of time and then, they were let to ripen for up to 14 days at 18 °C. Magness-Taylor’s was used as the standard method. Based on the Ho hypothesis, it was concluded that the methods do not have the same precision. However, a highly significant correlation coefficient r between the pairs of the individual methods allows to recalculate the results of one method by the results of the other method according to the linear y = a + bx formula. Correlation and regression coefficients varied in respect to the cultivar and growing season. The highest correlation coefficient (r > 0.890) between MT x F methods was observed for the pears with firmness below 20 N (measured by MT method). It may be concluded that the measurement method for the coefficient of elasticity using the Fekete instrument is particularly suitable for the firmness determination of elastic materials such as ripening pears, but it should not be recommended for the investigation of hard, freshly picked apples or pears.