In this study, a Geiger-Muller counter was used as a detector to measure the linear and mass attenuation coefficients (μm) for several polymers, including polypropylene (PP), polyethylene terephthalate (PET), high density polyethylene (HDPE), and polystyrene (PS). It was found that the linear attenuation coefficients were 8.6136, 35.1, 9.1169, 4.496 cm-1 for PP, PET, HDPE, and PS, respectively. Also, the mass attenuation coefficients (μm) were 10.074, 36.5, 9.698, 4.68 cm^2/g^3 for PP, PET, HDPE, and PS, respectively. Theoretically, the total atomic, electric cross sections, the effective atomic numbers (Zeff), HVL and TVL were computed using the values of mass attenuation coefficients (μm) that were obtained for the samples under study. The chosen polymers' theoretical values were found to be in perfect agreement with the earlier literature. The current study concluded that Polyethylene Terephthalate (PET) is the best shielding polymer material because it has more μm values than the other polymer materials.