Mechanical deformability of cells is an important property for their function and development, as well as a useful marker of cell state. The classical technique of micropipette aspiration allows single-cell studies and we provide here a method to measure the two basic mechanical parameters, elastic modulus and Poisson's ratio. The proposed method, developed from finite-element analysis of micropipette aspiration experiments, may be implemented in future technologies for the automated measurement of mechanical properties of cells, based on the micropipette aspiration technique or on the cell transit through flow constrictions. We applied this method to measure the elastic parameters of lymphocytes, in which the mechanical properties depend on their activation state. Additionally, we discuss in this work the accuracy of previous models to estimate the elastic modulus of cells, in particular the analytical model by Theret et al., widely used in the field. We show the necessity of using an improved model, taking into account the finite size of the cells, to obtain new insights that may remain hidden otherwise.