Flow-induced vibration and hydroelastic instability of parallel-plate assemblies are studied theoretically. A model of multi-parallel-beams joined with a single-beam is adopted in the theoretical analysis of the natural vibration characteristics of the parallel-plate assembly. In the theoretical calculation and analysis on the wet natural modes, the dry-modal functions are used as trial functions to solve the complex mode equation, utilizing the extended Galerkin method. Fluid-structure interaction on the parallel-plate assemblies is of complex-modal characteristics. Some regular results are d...