Micro-pipette aspiration technique is a widely used, non-destructive experimental method to determine the mechanical properties of cells and tissues. This experimentation is performed with the assumption of cells pertaining fluid-like characteristics, and the surface tension is determined through the mechanical response of the cell being deformed. In this work, living cells are described with the properties of hyperelasticity and poroelasticity, to study the response of these materials under the loading conditions of aspiration. The work put forth, builds on complexities by considering geometric non-linearities of contact between the continuum and the pipette, leading to understanding the effects of surface energy on continuum possessing hyperelasticity. This consideration highlights the variation in stiffness of the continuum with applied pressure, parameterized by elastocapillarity length scale. The reaction forces experienced by the continuum due to contact are also illustrated before incorporating the characteristics of poroelasticity, into mixed finite element formulation. The transition of stress, chemical potential and concentration of continuum exhibiting poroelasticity is presented. Lastly, the effects of surface energy on the continuum resembling living cells, characterized by poroelasticity are studied.