The objective of this study was an investigation of the material properties of the fresh pig kidney and parametric characterization of its elastic and inelastic material behavior. The material investigation included density measurements, uniaxial as well as three-dimensional compression tests, tensile tests. and shear tests on the samples extracted from the fresh pig kidney. For comparison, density measurements on a number of soft synthetic materials were also performed. Compression tests on the radial and the tangential specimens from the cortex tissue were performed at various loading rates. Three-axial compression tests were performed on the cortex tissues placed in a compression chamber. Shear tests were performed by punching a cylinder into a slice of the cortex. Tensile tests were carried out on the outer capsule. For characterization of the material behavior, a non-linear theoretical simulation based on a two parameter Blatz model was used. For characterization of the time-dependent behavior of the pig kidney cortex, a four-parameter linear viscoelastic model was employed. From the present experimental and theoretical studies, a number of conclusions were derived: (1) The general behavior of the pig kidney cortex samples under compression showed the general non-linear features typical of the soft tissues; the stress strain diagram was composed of a very flat part at very low stress level to about 30% relative deformation which was followed by a steeply rising stiffening leading to the radial rupture of samples marked by a maximum nominal rupture strain of about 50%. (2) The uniaxial compression tests on the radial and the tangential samples from the cortex tissue showed an increase of the rupture stress with the increase in the loading rate, but a decrease in the related rupture strain. (3) The long-term uniaxial compression tests on the cortex specimens under sustained constant load showed an instantaneous deformation followed by a creep response which eventually approached an asymptote. (4) Simulation of the non-linear material behavior of the cortex tissue under uniaxial compression by the Blatz model gave two pairs of material parameters for the cortex in the radial and the tangential directions. Furthermore, fitting of the assumed four-parameter linear viscoelastic model with the experimental data resulted in the viscoelastic material parameters.