Polymer composite materials (PCM) are used extensively and are viewed as candidates for application in various industries, including nuclear power. Despite a variety of methods and procedures employed to investigate the mechanical characteristics of PCMs, the use of the laboratory sample mechanical test results to design and model large-sized structures is not always fully correct and reasonable. In particular, one of the problems is concerned with taking into account the scale parameter effects on the PCM strength and elastic characteristics immediately in the product. The purpose of the study is to investigate the scale effects on the mechanical characteristics of glass reinforced plastics using phenolformaldehyde and silicon-organic binders and a fabric quartz filler. Samples of four different standard sizes under GOST 25604-82 and GOST 4648-2014 were tested for three-point bending using an LFM-100 test machine to estimate the scale effect. The thicknesses of the model samples were chosen with regard for the wall thicknesses of full-scale products under development or manufactured commercially and the test machine features, and varied in the limits of 1.6 to 7.5 mm. The tests showed that strength decreased as the sample thickness was increased to 3 mm and more both at room and elevated (200 to 500 °C) temperatures, which can be described by an exponential function based on the Weibull statistical model. The values of the Weibull modulus that characterizes the extent of the scale effect on the strength of the tested materials were 4.6 to 6.7. The average bend strength in the sample thickness range of 3 mm and less does not vary notably or tends to increase slightly as the thickness is increased. This fact makes it possible to conclude that estimation of allowable stresses in a thin-wall product requires the use of test results for samples with a thickness that is equal to the product wall thickness since standard samples may yield overestimated allowable stress values and lead, accordingly, to incorrect calculations of the strength factor. The results obtained shall be taken into account when defining the allowable levels of operation for full-scale products and structures of polymer composites based on the laboratory sample strength data as well as when estimating their robustness as a characteristic of the product’s fail-safe operation.