This study presents an investigation of the electrical and thermal conductivities of composites based on an ethylene vinyl acetate (EVA) copolymer matrix and nanostructured expanded graphite (EG). To improve the EG dispersion in EVA, EG sheets were modified by treating them with the anionic surfactant sodium dodecyl sulphate (SDS) in water. The modified SDS-EG platelets, after being filtered and dried, were melt-mixed with EVA to prepare the composites. Finally, both EVA/EG and EVA/SDS-EG composites were subjected to 50 kGy electron beam (EB) irradiation. SEM images confirm that the irradiated EVA/EG samples had improved interfacial adhesion, while the irradiated EVA/SDS-EG samples showed even better interfacial adhesion. The gel contents of the irradiated samples without and with SDS treatment increased with increase in EG loading. The EVA/EG composites exhibited a sharp transition from an insulator to a conductor at an electrical percolation threshold of 8 wt %, but with SDS-EG the electrical conductivity was extremely low, showing no percolation up to 10 wt % of filler. The EB irradiation had no influence on electrical conductivity. The thermal conductivity linearly increased with EG content, and this increase was more pronounced in the case of SDS-EG, but decreased after EB irradiation. The thermal properties were little influenced by EB irradiation, while better polymer–filler interaction and better filler dispersion as a result of SDS treatment, and the EB irradiation initiated formation of a cross-linked network, had a positive effect on the tensile properties. ; National Research Foundation of South Africa (UID 73982) and the International Bureau of the BMBF in Germany (project SUA 10/009).