In this work a tissue aspiration method for the in-vivo determination of biological soft tissue material parameters is presented. An explicit axisymmetric finite element simulation of the aspiration experiment is used together with a Levenberg-Marquardt algorithm to estimate the material model parameters in an inverse parameter determination process. Soft biological tissue is modelled as a viscoelastic, non-linear, nearly incompressible, isotropic continuum. Viscoelasticity is accounted for by a quasi-linear formulation. The aspiration method is validated experimentally with a synthetic material. In-vivo (intra-operatively during surgical interventions) and ex-vivo experiments were performed on human uteri.