Research on the viscous behavior of soft soils suggested that the effective stress should be divided into two components. One is related to the solid contacts between the grains, and its variation would be the true cause of deformations and distortions. The other is related to the viscous contacts of the water adsorbed to the grains, which would not cause deformations or distortions, and would be a function of the strain rate. This model is able to explain some phenomena, such as secondary consolidation and the increase in pore pressure after drainage closure. However, a consolidation theory adopting a linear relationship between the viscous component and the strain rate (Newtonian behavior) could not reproduce the secondary consolidation as seen in consolidation tests. In this paper, three theories of radial flow consolidation were developed and solved analytically. In two of them the linear relationship was adopted, while in the third one a non-linear relationship was proposed (non-Newtonian behavior). The solutions showed that the linear relationship is in fact not able to reproduce secondary consolidation, but the non-linear relationship provided much better results and can be a promising tool for future studies.