The aim of the study is to develop and perform a preliminary evaluation of a method for diagnosing and locating internal defects in multilayer polymer composite materials using non-destructive testing data. A method combining topological data analysis and graph-signal processing is proposed. To demonstrate the potential feasibility of this method, an analysis of synthetic ultrasonic signals was conducted. A set of 81 ultrasonic signals, representing various locations of internal defects in the composite material, was used. Topological data analysis enabled the identification of informative topological features and distinguished defective from defect-free cases with a silhouette score of 0.471. The results show the potential of using topological data analysis to automate the structural monitoring of internal defects in multilayer polymer composite materials.