The stress-deformation relation for three dimensional Maxwell model is proposed by the help of the semi-linear interrelation between the internal strain tensor, which gives the stress state, and the observable displacement tensor. The s–d relation is invariant for time dependent rigid rotation of the sample, while in the case of time dependent coordinate transformation there exist additional terms depending on the time-rate of transformation. As an example of the theory, the non-linear viscosity and the normal stresses are obtained introducing suitable parameters characterizing non-linear viscoelastic properties of the model. The results are qualitatively in good agreement with those of many experiments.