Annually, 1.5 billion tires—composed of up to 90% vulcanized rubber—are discarded worldwide. Due to its complex and cross-linked structure, vulcanized rubber is extremely difficult to recycle and reprocess. This study investigates the potential application of recycled rubber as a core material in sandwich composite structures. Given the potential use of these materials as structural elements, it is crucial to determine their operating stress limits. While design approaches in composite engineering typically rely on theoretical models and safety factors, the integration of additional testing methods enables more accurate insight into material degradation processes. Static tensile tests showed that the composite without rubber had a strength of approximately 120 MPa, whereas with the addition of 5% recycled rubber, a strength of approximately 100 MPa was achieved. Static tensile testing, conducted alongside acoustic emission (AE) monitoring, allows for identifying stress thresholds that correlate with increases in AE event counts, root mean square (RMS) values, or signal amplitude—parameters that signal structural changes within the composite during loading. The aim of this study was to establish allowable stress values for recycled rubber-based composites, considering different configurations of the rubber layer distribution using the AE method. Based on the read average values of the stresses at which damage is initiated in the composite materials, it is noticeable that despite the earlier values indicating better parameters of the K1 composite – 1 layer of rubber recyclate (64.8 MPa), comparable results are also obtained for the K3 – 3 layers of rubber recyclate (64 MPa) composite. Of the three tested materials, the K2 composite consisting of 2 layers of recyclate rubber is characterized by the lowest value (62.6 MPa).