In this article, the authors present the geometry and measurements of the properties of an acoustic metamaterial with a structure composed of multiple concentric rings. CAD models of the structure were developed and subsequently used in numerical studies, which included the study of resonant frequencies using the Lanczos method and an analysis of sound pressure level distribution under plane wave excitation using the finite element method. Subsequently, experimental tests were carried out on models with the same geometry produced with three different materials (PLA, PET-G, and FLEX) using a fused deposition modeling 3D printing technique. These tests included: determining insertion loss for a single model based on tests using the measurement window of a reverberation chamber and determining transmission loss through tests in a semi-anechoic chamber. Sound wave resonance was obtained for frequencies ranging from 1700 to 6000 Hz. Notably, the experimental studies were carried out for the same structure for which numerical tests were conducted. The physical models of a metamaterial were manufactured using three different readily available 3D printing materials. The results of laboratory tests confirm that the created acoustic metamaterial consisting of multi-ring structures reduces noise in medium and high frequencies.