This paper is devoted to the mathematical justification of the usual models predicting the effective reflection and transmission of an acoustic wave by a low porosity multiperforated plate. Some previous intuitive approximations require that the wavelength be large compared with the spacing separating two neighboring apertures. In particular, we show that this basic assumption is not mandatory. Actually, it is enough to assume that this distance is less than a half-wavelength. The main tools used are the method of matched asymptotic expansions and lattice sums for the Helmholtz equations. Some numerical experiments illustrate the theoretical derivations.1. Introduction. Perforated plates are widely used in engineering systems, either as resistive sheets for acoustic liners [24] or for cooling purposes at the walls of the combustion chambers of jet engines [19]. As these plates generally contain tens of thousands of holes for realistic geometries, the direct determination of the effect of the perforations is out of reach in numerical simulations. As a result, the effective acoustic behavior of such plates is usually reproduced by designing suitable semi-analytic models.Most of these models are based on the calculation of the Rayleigh conductivity of a hole, which relates the net fluctuating volume flux through the perforation to the fluctuating pressure drop across it (cf., e.g., [32,12]). Such an approach has several advantages. The most valuable of them is the possibility of coupling models taking into account the absorption of acoustic energy by viscosity at the orifices with the usual equations governing the propagation of acoustic waves elsewhere. The most frequently used model relies on the expression for the conductivity of a single circular hole in an infinitely thin wall derived by Howe [10]. In this model, a bias flow crosses the orifice. The limiting case, when the velocity of the bias flow goes to zero, is reduced to the very classical approach, earlier derived by Rayleigh [32]. In [35], one can find a clear derivation of the Rayleigh conductivity model for circular perforations in an infinitely thin plate, although formal and implicit as regards the method of matched asymptotic expansion. Howe's model was later extended to a hole in a thick plate [11,15]. These models are widely used in the literature for plates of low porosity