Waves and swell incident on a continuous cover of sea ice can become coupled to the ice and propagate as flexural-gravity waves. These ice-coupled waves are determined by a dispersion equation and attenuation coefficient which depend critically on the material properties of the sea ice. Two models of sea ice are proposed: - a linearly viscoelastic thin plate with uniform properties throughout; and a thermorheologically simple, viscoelastic thin plate whose properties vary through the ice sheet due to the temperature gradient across its thickness. Using the former model, an approximate solution consisting of the superposition of three ice-coupled waves is found for deep water waves impinging on ice at normal incidence. The characteristic properties of these waves are discussed in detail. The latter, more complicated model is developed and solved assuming that the viscoelastic Poisson's ratio is constant and the viscoelastic Young's modulus at a particular reference temperature satisfies some sea ice model proposed in the literature. Flexural-gravity wave solutions are discussed with emphasis laid on their temperature dependence and the effects of rotatory inertia and transverse shear. Obliquely incident waves are also considered. It is shown that the presence of significant attenuation within the ice cover leads to inhomogeneous flexural-gravity waves near the ice edge but the degree of inhomogeneity and angular spread decreases with distance. The existence of a critical angle of incidence enhances this effect considerably. Experiments carried out using strain measuring instruments on fast ice in Newfoundland are discussed and the data obtained are compared with theoretical predictions. It is shown that the direction and magnitude of wave components at some locations may be found using a rosette of three instruments but that large errors may occur in the subsequent data processing. A method avoiding these errors is proposed and implemented. Additional observations of ice-coupled waves recorded at Strathcona Sound are reported and possible mechanisms for their generation are suggested.