The non-linear behavior of dynamic viscoelasticity of plastic materials (e.g., plastic fat, butter, margarine, paraffin etc.) were investigated by means of a rotating rod method. The results were analyzed by using two phenomenological theories, i.e., Eyring's theory of rate process for non-Newtonian liquids and a mechanical model with slider element.In the former analysis the hole volume and activation energy of flow were calculated. It was found that the smaller value of the hole volume is accompanied by the larger values of the activation energy and of the stress at which the non-linear effect appears.In the latter analysis, the magnitudes of characteristic constants of spring, dashpot and slider were numerically determined. The model consists of two circuits of mechanical elements: the one is a parallel combination of a spring and a dashpot for describing the elasticity and viscosity in the range of linear deformation, and the other is a parallel combination of a spring, a dashpot and a slider for describing the elasticity, viscosity and yield value in the range of non-linear deformation.The tested materials contain fine crystalline particles which in amorphous medium, form a kind of network structure by the interlinkages. The observed non-linear deformation is probably caused by slippage between these interlinked crystalline particles.