In this study, polymer/glass fiber fabric‐based nanocomposite plates were fabricated with 0.01%–0.1% single‐walled carbon nanotubes (SWCNTs) and filler materials (barite, magnetite, and colemanite) using a hand layup process. Mechanical properties (e.g., tensile strength, flexural strength, and Charpy impact strength), thermal conductivity, and radiation shielding properties (e.g., gamma radiation and neutron radiation) of the specimens were determined. The results revealed that the specimens containing barite and magnetite managed to exhibit adequate mechanical properties (especially Charpy impact strength). Among different filler materials used, barite‐filled specimens outperformed colemanite and magnetite‐filled specimens in terms of mechanical properties. The mechanical performance of filler‐modified specimens can be further enhanced by adopting efficient dispersion techniques to disperse filler material and SWCNTs throughout the composite plates. The thermal conductivity of barite, magnetite, and colemanite‐filled specimens (with/without SWCNTs) increased by 30.56%–60% as compared to specimens only containing SWCNTs and neat polymer, which avoids the accumulation of heat required for radiation shielding applications. Similar to thermal conductivity, specimens containing filler materials (with and without SWCNTs) provided higher gamma and neutron radiation shielding properties as compared to neat polymer‐ and SWCNT‐modified specimens. In the case of gamma and neutron radiation shielding, barite‐ and colemanite‐filled specimens provided better results, respectively.