Complex signal processing functions can be performed by acoustic wave correlators, with simple structures, through the variation of electrode patterns. Numerical simulations of Surface Acoustic Wave (SAW) correlators, previously limited to analytical techniques like delta function and equivalent circuit models, require simplification of second order effects such as backscattering, charge distribution, diffraction, and mechanical loading. With the continual improvement in computing capacity, the adaptation of finite element modelling (FEM) is more efficient for full scale simulation of electromechanical phenomena without model oversimplification. This is achieved by resolving the complete set of partial differential equations. In this paper a novel way of modelling a 3-dimensional acoustic wave correlator using finite element analysis is presented. This modelling approach allows the consideration of different code implementation and device structures. This is demonstrated through the simulation results for a Barker sequence encoded acoustic wave correlator. The device response for various surface, bulk, and leaky modes, determined by the excitation frequency, are presented. Moreover, the ways in which the gain of the correlator can be optimised though variation of design parameters is also outlined.