The transmission of sinusoidal vibrations through beds of wet sands has been measured. Results have been interpreted in terms of a Critical State model to predict a function of the elastic swelling constant, k(1), and the cohesive compressive stress u(c). Factors affecting k(1) and u(c) have been considered with emphasis on moisture content, particle size distribution and bulk density. Surfaces of k(1) and u(c) have been produced in % moisture/% fines space. The results have been interpreted in terms of liquid bridge bond models, with application to the structure and strength of wet agglomerates. u(c) is isotropic and dependent only upon bulk properties, whereas the elastic k(1) is strongly affected by both bulk properties and boundary conditions. This has implications for the investigation of the properties of wet agglomerates.