Quantitative characterization of viscoelastic properties in biofilms and other soft materials are crucial to understanding the origin of their dynamic heterogeneous architecture, mechanical stability, and mechanical responses to external stimuli. The optical coherence elastography (OCE) technique recently emerged as a powerful nondestructive characterization tool that relies on low coherence interferometry for measurement of elastic wave propagation in transparent media. In this lecture, I will present a frequency domain OCE approach that facilitates measurement of the dispersion relation of guided transverse waves in soft transparent materials. I will discuss the numerical modeling approach that we adopted to predict the dispersion relation of viscoelastic transverse wave modes in flat plates, curved plates, and semi-infinite substrates, subjected to different boundary conditions. The model provides a useful tool to study the sensitivity of the wave speed to various properties including, viscoelastic properties, hydrostatic pressure, thickness, curvature, and density, for inverse analysis of mechanical properties, and to select experimental parameters for optimal sensitivity. I will present experimental results and numerical calculations that demonstrate how my research group has applied the combination of the modeling approach and the frequency domain OCE measurements to characterize the viscoelastic properties of various hydrogels and environmental biofilms, and the hydrostatic pressure-dependent mechanical properties of corneal tissue phantoms.