This dissertation mainly investigates the dispersion, attenuation, and energy dissipation of ultrasonic guided waves propagating in an elastic plate with excessive damping. The excessive attenuation caused by the thermoelastic coupling of plate or the external viscous fluid loading on the top surface of plate is taken into account. The former represents the damping resulted from the time derivative of state variables in a dynamic system, but the later denotes the intrinsic damping term in the elastic constants. Owing to the above two different excessive damping, the investigation is divided into two works. Thermoelastic waves propagating in an isotropic thin plate exerted by a uniaxial tensile stress are represented in the first work. Characteristic equation of thermoelastic guided waves is formulated based on the theory of acoustoelasticity and classical thermoelasticity. Curve tracing method for complex root-finding is used to determine the attenuation, which is the imaginary part of the complex-value wavenumber. It is found that each plate mode of thermoelastic wave propagating in an isotropic plate with or without pre-stress has a minimum attenuation at a specific frequency except the A0 mode. These modes are called by the Lamé modes, which are the volume resonances in the thickness direction and propagate along the plate with the least energy dissipation. Frequency spectra of the phase velocity dispersion and attenuation of thermoelastic waves propagating along various orientations in the uniaxial pre-stressed thin plate have further been discussed. The second work describes an investigation of acoustic guided wave propagation in a glass plate overlain with a poly-vinyl-alcohol (PVA) layer. The PVA layer is modeled as a hypothetical isotropic solid with dynamic viscosity. Dispersion and attenuation curves, mode shape, trajectories of surface particles on the substrate, and pressure in the fluid layer are studied numerically. Except for the A0 mode, a steeply decreasing attenuation and a reverse trajectory of motion are observed near the frequency of Lamé mode for the different modes. With increasing frequency, displacement, stress, and energy of the A0 mode are significantly confined to a region near the top surface of the plate. A similar phenomenon occurs near the bottom surface for the S0 mode. The pressure gradient and its distribution in the fluid layer are directly related to the trajectories of surface particles on the interface of fluid and substrate. The symmetric modes, except for the S0 mode, at frequencies corresponding to the maximum group velocity, are the appropriate choices for generating uniform acoustic pressure in the fluid layer. Moreover, a glass substrate overlain with a glycerin layer is also taken in account, and its frequency spectra of the phase velocity dispersion and attenuation have further been discussed.