We consider two problems in boundary controllability of coupled wave/Kirchoff systems. Let Ω be a bounded region in , n2, with Lipschitz continuous boundary Γ. In the motivating structural acoustics application, Ω represents an acoustic cavity. Let Γ₀ be a flat subset of Γ which represents a flexible wall of the cavity. Let z denote the acoustic velocity potential, which satisfies a wave equation in Ω, and let v denote the displacement on Γ₀, which satisfies a Kirchoff plate equation on Γ₀. These equations are coupled via ∂z/∂ν=v_t on Γ₀ (where ν is the exterior unit normal to Γ₀), and the backpressure—z_t appears in the Kirchoff equation. In the first problem, we consider a control u₀ in the Kirchoff equation on Γ₀, and an additional control u₁ in the Neumann conditions on a subset Γ₁ of Γ, where ΓΓ₁ satisfies geometric conditions. Using both controls, we obtain exact controllability of the wave and plate components in the natural state space. In the second problem we consider only the control u₀. Without geometric conditions, exact controllability is not possible, but we show that for any initial data, we can steer the plate component exactly, and the wave component approximately.