Measurement of cell stiffness, which results from changes in the cytoskeletal structure of cancer cells, can be used as a promising approach for the early detection of cancer. One of the methods for investigating the mechanical properties of the cell surface is the use of atomic force microscopy (AFM), which can be used to determine the stiffness of the cell membrane by indenting the cell. From a biomechanical point of view, cancer can be investigated by determining the Young’s modulus of cancer tissue. The determination and measurement of Young’s modulus in cancer cells can be performed either experimentally or using mathematical modeling approaches. In this study, Young’s modulus of cells is determined by analyzing force-indentation curves from experimental studies. For this purpose, force- indentation data measured with the AFM are used for two cell types: healthy and cancerous cervical and prostate cells. The mechanical contact models of Hertz, JKR and Tatara are then applied to the data to calculate the Young’s modulus. The results of these three models show that the Young’s modulus values obtained with the Hertz and Tatara models are very close to each other, while the value obtained with the JKR model is significantly lower. This discrepancy is attributed to the inclusion of adhesion forces in the JKR model. Based on the results of this study, the difference in Young’s modulus between cancerous and healthy cells could serve as a potential indicator for early cancer detection.