Due to their major qualities, including light weight, fracture toughness, increased stiffness, and impact energy absorption capacity, thin-walled structures composed of nanocomposite materials may be used as energy-dissipating parts in automobiles. The current study aims to evaluate the transverse deformation performance of glass/nano-silica/epoxy GFRE composite cylinders subjected to quasi-static lateral loadings. All representative samples’ crush profiles and force-displacement curves during crushing were documented and discussed. For the studied specimens, the absorbed energy (AE) and the specific absorbed energy (SEA) were evaluated and recorded. Also, mathematical regression models were built to predict the energy absorption indicators. Based on the experimental results, the inclusion of SiO2 significantly reduced AE and SEA.