Thin plates, in the form of individual panels or whole device casings, often separate the noise source from its recipients. It would be very desirable if the panels could effectively block the sound transmission preventing noise from further propagation. This is especially challenging to achieve at low frequencies. A promising approach, intensively developed in the recent years, is to employ active control methods by adding sensors and actuators, and running a control algorithm. However, if the noise is narrow-band, an alternative passive solution originally developed by the authors can be applied. It is based on appropriately located passive elements which can be used to alter the frequency response of the vibrating structure thus improving its sound insulation properties. Such an approach is referred to as the frequency response shaping method. The purpose of this paper is to further develop this method and apply it to a device casing panel. The efficiency of the method is evaluated by simulation and real experiments. Appropriate cost functions and mathematical models are formulated and used to optimise the arrangement of passive elements mounted to the plate, enhancing its sound insulation properties at the given frequency range. The results are reported, and advantages and limits of the method are pointed out and discussed.