This paper presents and compares two different approaches to solving the problem of wave propagation across a large finite periodic array of surface-piercing vertical barriers. Both approaches are formulated in terms of a pair of integral equations, one exact and based on a spacing δ > 0 between adjacent barriers and the other approximate and based on a continuum model developed formally using homogenisation methods for small δ. It is shown that both formulations possess the same mathematical structure, the approximate method being simpler to evaluate than the exact method which requires eigenvalues and eigenmodes related to propagation in an equivalent infinite periodic array of barriers. In both methods, the numerical effort required to solve problems is independent of the size of the array. The comparison between the two methods allows us to draw important conclusions about the validity of homogenisation models of plate array metamaterial devices. The practical interest in this problem stems from the result shown in this paper that there exists a critical value of radian frequency, ωc , dependent on δ, below which waves propagate through the array and above which results in wave decay. p For δ → 0, the critical frequency is given by ωc = √ (g/d) where d is the plate submergence and g is gravity which relates to resonance in narrow channels. The results have implications on proposed schemes to harness energy from ocean waves and other problems related to rainbow trapping.