Characterization of the viscoelasticity for soft tissues is useful for medical diagnosis. Various ultrasound and magnetic resonance-based techniques have been developed over the past few decades. With ultrasound methods, generating and tracing a shear wave (SW) propagating within the soft tissue was one of the promising approaches to measure the SW velocity and absorption, which were the key parameters to derive the tissue viscoelasticity. When the SW method was employed, several problems, such as undesired SW reflection, motion artifact and SW diffraction could occur in practical experimental configuration, which caused on SW measurements. Advanced ultrasound imaging system with high frame rate may be able to overcome these problems, yet the configuration of such system was complex and thus expensive. In this thesis, methods to solve the above-mentioned problems were proposed by using conventional ultrasound imaging system with a relatively less complex design and low frame rate. In the proposed methods, the undesired SW reflections were able to be distinguished and removed from the observed SW in the spatial domain using the scanning time delay in the B-mode measurement of conventional ultrasound system. The causes of the motion artifact were examined through the temporal domain analysis, and temporal frequency filter was used to reduce the undesired motions. In addition, the measurement configuration to minimize the diffraction effect on the SW measurement was investigated. Furthermore, a numerical method to compensate the diffraction effect was developed for the absorption measurement. The effectiveness of these proposed methods was verified by numerical simulations as well as by experiments using soft-tissue mimicking phantom specimens. The proposed methods were finally applied for in-vivo measurements and successfully demonstrate the stiffness difference of an upper arm muscle with and without muscle contraction.