The response of regular arrays of two-dimensional Helmholtz resonators mounted in a rigid baffle and subject to external excitation by a plane acoustic wave is studied. The inviscid. The inviscid linearized problem is solved by the matched-asymptotic-expansion technique in the low-frequency limit, i.e. when the characteristic neck dimension is small compared with the acoustic wavelength. Different spacings between resonators, from comparable with down to much smaller than the wavelength, as well as variable neck length and different cavity shapes, are studied without assumptions about the velocity distribution in the neck. The results yield predictions of resonance for the different geometries and compare favourably with measurements. Besides showing analytically the dependence, of, say, the acoustic impedance on all geometric parameters and forcing frequency, the analysis also reveals that for deep narrow cavities the basic Helmholtz model with uniform cavity pressure is inappropriate at resonance.