In the design of table top phones that contain loudspeakers, for instance conference phones, it is desirable to minimize feedback from the loudspeaker to the microphone. The current work concerns the feedback from the loudspeaker to the microphone through the casing. The final aim is to find a design of the casing that minimizes the structural feedback. A simplified model of the casing, a thin plate, is considered in this preliminary investigation. Laterally uniform deflections of the plate are modelled as the dynamic Euler–Bernoulli beam loaded at the boundary. The simulation results are verified against 3D structural mechanics solutions from COMSOL 4.2. The thickness distribution of the beam model is numerically optimized in order to minimize the vibrations at a selected region of the beam. A lower limit and a upper limit for beam thickness, as well as the beam weight is used as optimization constraints. A static compliance constraint is also tested. The simulations show that it is possible to move structural vibrations both in the frequency space and in the spatial space. Vibration reduction up to 20 dB of certain frequencies at the microphone position can be obtained.