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This thesis will focus on the modelling and quantification of the mechanical properties of biological samples with the aid of Atomic Force Microscopy (AFM). The importance of studying the mechanical properties of biological samples lies in its potential use for both therapeutic and diagnostic research as well as in bioengineering fields such as designing/selecting appropriate cell sorting and separation techniques. First part of this thesis is focused on developing a mathematical model by considering the physical properties (size and membrane thickness) of cells, to measure the size changes and Young’s elastic modulus of mammalian cells. Developed model showed promising results in measuring the changes in the radius of the cells after deformation. Also, it has been showed that there is a direct relation between the shape of the indenter and obtained elastic modulus. Moreover, the Young’s elastic modulus derived from fitting the developed model into force-indentation curves was in the range of MPa. This is due to measuring the elastic properties of cells on the surface elements (lipid bilayer). Producing manufactured red blood cells (RBCs) is increasing due to the high demand for blood transfusions and lack of eligible donors. Manufactured RBCs require continuous sorting and separation process during their production, as well as at the end of the manufacturing process, where reticulocytes are formed. Selecting appropriate sorting and separation methods, which are highly efficient and have the minimum drawback, is essential. Techniques which are carry out the cell separation processes based on the mechanical and physical properties of cells shows promising results. Therefore, the second part of this thesis was designed to measure the mechanical and physical properties of CD34+ stem cells during their expansion and differentiation processes (Days 11, 14, 18 and 21) for cell purification and separation purposes. Obtained results showed that size-based techniques can be applied to sort cells at day 11 of differentiation process from the day 14, while for sorting day 14 cells from day 18 and day 18 cells from day 21, any elasticity or sized based techniques cannot provide a highly purified/sorted culture and significant contaminations would be remained. In addition, the mechanical properties of the extruded nucleus from the CD34+ cells was also quantified for studying their effects on the elastic properties of the CD34+ cells. Derived results showed that to eliminate the free-floating nucleus form the culture media, elasticity and size-based techniques can be used and provide a high efficient sorted culture (100% separation).