A new method for measuring the mechanical properties of soft biological tissues is presented. Dynamic testing is performed using a torsional resonator, whose free extremity is in contact with a tissue sample. An analytical model of a semi-infinite, homogenous, isotropic medium is used to model the shear wave propagation in the material sample and allows determining the complex shear modulus of the soft tissue. By controlling the vibration amplitude, shear strains of less than 0.2% are induced in the tissue so that the material response can be considered as linear viscoelastic. Experiments are performed at different eigenfrequencies of the torsional oscillator and the complex shear modulus is characterized in the range 1-10 kHz. In vitro experiments on bovine and porcine liver are presented in order to demonstrate the sensitivity of the proposed technique, and the reliability of the measurements is confirmed with comparative tests on synthetic material. The experiment does not damage the soft tissue and allows a fast and local measurement, these being prerequisites for future applications in vivo during open surgery.