An amplitude analysis of the $K_{S}K_{S}$ system produced in radiative $J/psi$ decays is performed using the $(1310.6pm7.0)times10^{6}$ $J/psi$ decays collected by the BESIII detector. Two approaches are presented. A mass-dependent analysis is performed by parameterizing the $K_{S}K_{S}$ invariant mass spectrum as a sum of Breit-Wigner line shapes. Additionally, a mass-independent analysis is performed to extract a piecewise function that describes the dynamics of the $K_{S}K_{S}$ system while making minimal assumptions about the properties and number of poles in the amplitude. The dominant amplitudes in the mass-dependent analysis include the $f_{0}(1710)$, $f_{0}(2200)$, and $f_{2}^prime(1525)$. The mass-independent results, which are made available as input for further studies, are consistent with those of the mass-dependent analysis and are useful for a systematic study of hadronic interactions. The branching fraction of radiative $J/psi$ decays to $K_{S}K_{S}$ is measured to be $(8.1 pm 0.4) times 10^{-4}$, where the uncertainty is systematic and the statistical uncertainty is negligible.
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