In this work an approach to implement multiple scattering theory for achieving analogue of elastic wave computing devices is presented. The outlined methodology is based on using elastic beams, supporting flexural wave propagation, as substrates to transfer signals and a set of point reflectors to manipulate energy flow. The role of the cluster of reflectors is to obtain desired transmission properties of the system. In particular, it is shown that an analogue of a logic gate can be achieved with such setup. First, an Euler-Bernouli beam theory is employed for calculating transmission and reflection coefficients for elastic wave scattering at a cluster of scatterers and the relation between the cluster geometrical and impedance properties is found. The design process is based on an optimization strategy. Namely, an optimization algorithm is used to obtain the optimal values for the geometry of the cluster and reflectors’ properties to achieve desired transmission and reflection coefficient values. Additionally, a penalty function is introduced to prevent physically impossible scenarios. As an example, the optimization procedure is carried out to obtain an XOR gate functionality and extended further to achieve binary half-adder and full-adder functionalities. The proposed method provides a more accurate and efficient way to perform calculations with analog signals without the need of it’s beforehand conversion to a binary state. The results demonstrate the potential for using this approach in practical applications such as in the design of micro-electromechanical systems (MEMS).