The aspiration technique is used to characterize the mechanical behavior of soft human tissues. This method has been applied intra-operatively on human liver as well as on the uterine cervix during gestation. Further applications are on other abdominal organs as well as on the vaginal wall. The experimental set-up, the measurement protocol and the procedure for data analysis are described in this paper. Application on human organs aimed at (i) tissue classification towards development of novel diagnostic procedures, and (ii) determining constitutive models of soft biological tissue. The first goal is achieved using scalar parameters extracted from pressure and deformation profile histories. Determination of parameters for non-linear time dependent constitutive model formulations requires solving the inverse problem. Observations from on-going and recently completed clinical studies on liver, uterine cervix and vaginal wall are summarized in order to illustrate advantages and limitations of the aspiration technique.