The mechanical properties of yeast play an important role in many biological processes, such as cell division and growth, maintenance of internal pressure, and biofilm formation. In addition, the mechanical properties of cells can indicate the degree of damage caused by antifungal drugs, as the mechanical parameters of healthy and damaged cells are different. Over the past decades, atomic force microscopy (AFM) and micromanipulation have become the most widely used methods for evaluating the mechanical characteristics of microorganisms. In this case, the reliability of such an estimate depends on the choice of mathematical model. This review presents various analytical models developed in recent years for studying the mechanical properties of both cells and their individual structures. The main provisions of the applied approaches are described along with their limitations and advantages. Attention is paid to the innovative method of low-invasive nanomechanical mapping with scanning ion-conductance microscopy (SICM), which is currently starting to be successfully used in the discovery of novel drugs acting on the yeast cell wall and plasma membrane.