In this study, the viscoelastic properties of porcine kidney in the upper, middle and lower poles were investigated using oscillatory shear tests. The viscoelastic properties were extracted in the form of the storage modulus and loss modulus in the frequency and time domain. Measurements were taken as a function of frequency from 0.1 Hz to 6.5 Hz at a shear strain amplitude of 0.01 and as function of strain amplitude from 0.001 to 0.1 at a frequency of 1 Hz. Measurements were also taken in the time domain in response to a step shear strain. Both the frequency and time domain data were fitted to a conventional Standard Linear Solid (SLS) model and a semi-fractional Kelvin–Voigt (SFKV) model with a comparable number of parameters. The SFKV model fitted the frequency and time domain data with a correlation coefficient of 0.99. Although the SLS model well fitted the time domain data and the storage modulus data in the frequency domain, it was not able to capture the variation in loss modulus with frequency with a correlation coefficient of 0.53. A five parameter Maxwell–Wiechert model was able to capture the frequency dependence in storage modulus and loss modulus better than the SLS model with a correlation of 0.85.