Abstract: The paper deals with the definition and representation of objective stress rates. At first the requirement in symmetry to the form of the objective stress rates is given up and a family of generalized stress rates is defined. From the Cauchy fundamental principle of stress, two new unsyrnmetric objective stress rates are derived through objective rates of stress vectors, these rates are in form independent of deformation and deformation rate. The new objective stress rates represent the true change of the s...