We present newly reduced archival radio observations of SN 1996cr in the Circinus Galaxy from the Australia Telescope Compact Array and the Molonglo Observatory Synthesis Telescope, and attempt to model its radio light curves using recent hydrodynamical simulations of the interaction between the supernova (SN) ejecta and the circumstellar material (CSM) at X-ray wavelengths. The radio data within the first 1000d show clear signs of free-free absorption (FFA), which decreases gradually and is minimal above 1.4GHz after day ~3000. Constraints on the FFA optical depth provide estimates of the CSM free electron density, which allows insight into the ionization of SN 1996cr's CSM and offers a test on the density distribution adopted by the hydrodynamical simulation. The intrinsic spectral index of the radiation shows evidence for spectral flattening, which is characterized by {alpha}=0.852+/-0.002 at day 3000 and a decay rate of {Delta}{alpha}=-0.014+/-0.001yr^-1^. The striking similarity in the spectral flattening of SN 1987A, SN 1993J and SN 1996cr suggests this may be a relatively common feature of SNe/CSM shocks. We adopt this spectral index variation to model the synchrotron radio emission of the shock, and consider several scalings that relate the parameters of the hydrodynamical simulation to the magnetic field and electron distribution. The simulated light curves match the large-scale features of the observed light curves, but fail to match certain tightly constraining sections. This suggests that simple energy density scalings may not be able to account for the complexities of the true physical processes at work, or alternatively, that the parameters of the simulation require modification in order to accurately represent the surroundings of SN 1996cr.