In vacuo structural dynamics involves estimation of the structural responses due to structural forces and moments. Herein, the effect of the ambient fluid is ignored. In the field of structural acoustics, the structure is assumed to be in the ambience of an acoustic fluid. The acoustic pressure acts as an additional loading on the structure. This leads to the coupled structural acoustic formulation. Numerical simulation techniques are commonly employed for solution of such problems. Very few analytical solution procedures are available in the literature. Crighton made significant contributions towards analytical structural acoustics. In particular, he investigated the coupled structural acoustics of a semi-infinite plate immersed in an acoustic half space and subjected to line harmonic loading. In the present work, we extend the solution procedure for constrained semi-infinite plate. The effect of constraints is incorporated in the formulation in terms of unknown reaction forces and moments. These lead to additional flexural waves. The unknown reactions are determined by imposition of the kinematic constraint. The analytical solutions obtained using the present formulation is shown to have excellent correlation with solutions obtained using a commercial Finite element package. Interesting physical insights are drawn based on the analytical solution. © INTER-NOISE 2018 - 47th International Congress and Exposition on Noise Control Engineering: Impact of Noise Control Engineering. All rights reserved.