Four sets (A, B, C and D) of two-dimensional island platinum films [2D-I(Pt)Fs] were prepared by the thermal evaporation technique. The mass thicknesses for the films of such sets are 1, 5, 10 and 20 , respectively. The frequency-independent parameters of one of the equivalent circuit for island metal films in general are R (b), R (g) and C (g) where R (b) is the resistance of the islands themselves while R (g) is the resistance that accompanies the transfer of electrons across the gaps among islands and C (g) is the capacitance that results from the separated metallic islands. The least-square values of R (b), R (g) and C (g) for our films were deduced via a computerized analysis. The stabilized films were exposed to gamma-rays at doses 100, 200, 300, 500 and 700 Gy using (137)Cs (0.662 MeV) radiation source of dose rate 0.5 Gy/min. It was found that (1) For any particular mass thickness: (a) R (b) and R (g) decreases with the increase in the dose of gamma-rays while C (g) increases (b) the absolute value of the fractional change in R (b), R (g) and C (g) increases with the increase in dose. (2) For any particular dose the increase in the fractional change in R (b), R (g) and C (g) becomes more pronounced when the mass thickness increases. Qualitative interpretation for our results was given on the ground that gamma-rays changed the island's shape from spherical to prolate spheroid one and this has been checked experimentally via imaging the films by Atomic Force Microscope before and after gamma-irradiations.