An elastic shell model has been developed to describe the properties of beds of cohesive materials, A core comprises the elastic component of the Cam-Clay model, which is mean stress dependent, non-linear, and volumetrically elastic, It is surrounded by a thin, linearly elastic shell. This model is in agreement with structural models of wet agglomerates proposed by Sherrington and Butensky and Hyman, The model has been used to predict the natural frequency of a bed of material surmounted by a top cap mass. In general, both the elastic shell and the core contribute to the natural frequency. The model has been applied to the resonance frequency data for wet sands, coal and terephthalic acid (TA). The properties of these materials are dominated by the elastic shell. A scale-up rule developed from the model is able to predict resonance frequency for a range of sample sizes and shapes,