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Currently, there is a noticeable trend of modifying new materials by using additives from the recycling of harmful waste. This is to protect the environment by using waste to produce composites and at the same time to reduce the cost of their production. The article presents an analysis of the impact of the use of rubber recyclate obtained from the utilization of car tires as a sandwich layer of epoxy–glass composites and its impact on the strength parameters of the composite. The presented research is an extension of the previously conducted analyses on composite materials modified with the addition of rubber recyclate. The four variants of the materials produced contained the same percentage amount of rubber recyclate, but differed in the way it was distributed and the number of layers. Static tensile tests as well as impact strength and kinetics of damage to samples made with and without the addition of recyclate were carried out. Observation of the structures of the materials with the use of SEM was also performed. A significant influence of the method of distributing the recyclate in layers on the strength parameters of the materials was found. In the case of composites with three and two sandwich layers of recyclate, more favorable results were obtained compared to the blank sample. In addition, the values of the impact strength measurements were subjected to statistical analysis at the significance level of α = 95%. The distributions were tested for normality with the Shapiro–Wilk test, differences between pairs were tested with the Student's t-test for dependent groups, and ANOVA differences were tested for independent groups. Using the Student's t-test, it was confirmed that between the pairs of variables in the configurations reference sample and modified sample, there were significant statistical differences in the distribution of impact strength measurement results for all the analyzed materials. Statistical analysis showed a significant usefulness in the selection of the material with the best strength parameters and a significant role of statistical methods in the study of anisotropic materials. [ABSTRACT FROM AUTHOR]