Spherical cellular aggregates are in vitro systems to study the physical and biophysical properties of tissues. We present a novel approach to characterize the mechanical properties of cellular aggregates using a micropipette aspiration technique. We observe an aspiration in two distinct regimes: a fast elastic deformation followed by a viscous flow. We develop a model based on this viscoelastic behavior to deduce the surface tension, viscosity, and elastic modulus. A major result is the increase of the surface tension with the applied force, interpreted as an effect of cellular mechanosensing.