An experimental method for studying the residual stresses of products made of polymer composite materials (PCMs) is considered. The test scheme used is in agreement with the tests recommended for the pipes made of glass-fiber-reinforced plastics (GFRPs) according to the API15LR specification. An experimental relationship is established between the frequency and phase shifts of the wave front in the signals from two sensors in the study area, which makes it possible to associate it with the physical and mechanical characteristics of the material. A research algorithm is presented and an analysis method for detecting the zones of residual stresses is developed by the example of a TSK 130 pipe branch from GFRP. An experimental method is proposed for relating the changing of the partial frequencies in the local area of a PCM with the value of residual stresses in the product during its manufacture.