The propagation of sound waves in thin gas or fluid layers can be significantly affected by viscothermal phenomena. In this paper, a new viscothermal acoustic finite element is presented. The element includes the effects on inertia, viscosity, compressibility and thermal conductivity. The acoustic element can be coupled to flexible structural elements. This enables fully coupled acousto-elastic calculations to be made for complex geometries. The model is experimentally validated with measurements on a rigid airtight box with a flexible coverplate. Eigenfrequencies, damping and mode shapes of the plate were measured and compared with numerical results for a number of gas layer thicknesses. The agreement between measurements and calculations is good. The results indicate that there can be large shifts in eigenfrequency as a function of the layer thickness. In addition, for small layer thicknesses a high damping value is found, which can be attributed to viscous effects in the layer.