The micropipette aspiration experiment remains a widely used micromanipulation technique for quantifying the mechanical properties of biological samples. Our study extends previous results by investigating the influence of sample size and adhesion area on the mechanical response of compressible thin biological samples. We thus defined a nonlinear relationship between aspirated length, Young's modulus, Poisson's ratio and sample thickness which allowed us to develop an original experimental protocol for simultaneous quantification of the Poisson's ratio and Young's modulus of adherent samples. We first validated our method by characterizing mechanical properties of Polyacrylamide gels with tunable stiffness. We then considered application of these results to the quantification of cell elasticity, focusing on the influence of cell adhesion area onto the measured apparent cell stiffness.