We proposed a technique for measurements of the viscoelastic properties of soft tissues applying shear standing waves to the studied material. The technique is based on the resonator method developed and described in detail previously. In this method, the resonator was represented by the layer of studied material firmly connected between two parallel plates of finite mass. Accelerations of the plates could be measured by small and light uniaxial accelerometers. The vibrator forces one of the plates, while the layer forces the other. Arbitrary function generator powers the vibrator. Signals measured by accelerometers are evaluated in LabVIEW by a special algorithm, which is designed to maintain given acceleration amplitude on the vibrator and collect data for steady-state oscillations. Thus, we obtain the resonance curves in the range 1-500 Hz, showing the fundamental resonance and several more further resonances. We compare the resonance curves with the model of nonlinear resonator considering the material relaxation times. In this model, the wave from the plate forced by the vibrator interacts with the wave reflected from the opposite plate and standing wave is excited. This standing wave on the fundamental frequency tends to have a node in the area of the plate forced by the vibrator, whereas antinode is near the plate forced by the layer. The fundamental frequency depends on the viscoelastic properties of studied material and mass of the plate forced by the layer. Since frequency dependence on the plate mass lets one perform series measurements, it makes suggested method robust. We tested our technique "ex vivo". Measured values of shear moduli and shear viscosity correspond to the values for corresponding tissues found in literature. The further investigation will adapt the technique for "in vivo" measurements. In that case a novel inexpensive noninvasive technique applicable to tissue state control in human body will appear.