Elastography or elasticity imaging seeks to provide non-invasive quantitative systems that can measure or image the local mechanical properties of tissue, in order to enhance the accuracy of diagnosis, especially at early stages of disease. Elastography methods generally use a source of mechanical motion (vibration source) to probe the interrogated medium (tissue) through which the waves (vibration) propagate. The acoustic radiation force generated by an ultrasound source, provides an attractive means of creating a highly localized source within the tissue in a non-invasive manner. This localized force field can subsequently give rise to low-frequency shear waves, which are known to travel slowly (at 1-10 m/s) within soft tissue and to possess highly dispersive properties. An effective way in which localized low-frequency shear waves can be generated, is by the modulated (oscillatory) radiation force resulting from the interference of two quasi-CW ultrasound beams of slightly different frequencies. Such waves will be narrowband rather than broadband and thus, will suffer less from the effects of dispersion, enabling the shear speed and attenuation to be estimated as functions of frequency. This can be achieved by tracking the shear-wave phase delay and change in amplitude over a propagated distance. Measurements at different frequencies can then be fitted to a viscoelastic model (e.g. the Voigt model), enabling the tissue elasticity and viscosity to be extracted. The properties of the narrowband shear wave propagation in soft tissue are studied by using the Voigt viscoelastic model and Green's functions. In particular, the manner in which the characteristics of the viscoelastic medium (i.e., the shear modulus and viscosity) affect their evolution is investigated under both low-amplitude (linear) and high-amplitude (nonlinear) source excitation and conditions that conform to human safety standards. Methods of estimating the local viscoelastic properties of the propagating medium are also proposed.