Due to recent developments in additive manufacturing, architectured metamaterials with specific microstructure are widely studied due to the large range of available designs and corresponding effective properties. In this paper, a periodic structure based on a periodic arrangement designed by F. Dos Reis et al(F. Dos Reis, J.F. Ganghoffer, Equivalent mechanical properties of auxetic lattices from discrete homogenization, Comp. Mat Sc., 51 :314?321, 2012), is studied. Depending on various geometrical parameters, the structure may exhibit in certain cases an effective negative Poisson?s ratio (auxetic structure) or an effective positive Poisson?s ratio greater than 0.5 (anti-auxetic structure). In the first part of the paper, an analytical discrete homogenization scheme using an Euler-Bernoulli model is briefly presented. Then, a numerical homogenization method, based on the finite element method and using Christoffel?s equation inversion model, allows the determination of the effective anisotropic elastic tensor. The agreement between the two models and their limitations are discussed. Then, experimental data are obtained on thin micro-structured plate realized using 3D additive printing. Static characterization with tensile tests gives effective Poisson?s ratio whereas a dynamic analysis shows the identification of eigenfrequencies of the plate and the validity limit of the homogenization technics. Finally, the potentialities of a panel based on this architectured structure are studied for underwater absorption application in terms of reflection, transmission and absorption coefficients.