The elastoplastic constitutive analysis which utilizes the model of mu
ltiplicative decomposition of the deformation gradient into its elasti
c and plastic parts has been mainly developed and applied to elastical
ly isotropic materials, which remain isotropic during the process of p
lastic deformation. This paper extends the application of the model to
materials that change their elastic properties during the deformation
process as a result of the material degradation and the corresponding
damage. The exact kinematic and kinetic analysis of the finite deform
ations leads to an additive decomposition of the total strain rate int
o its elastic, damage and plastic constituents. The general structure
of the expression for the damage strain rate is derived, valid for uti
lized damage tensors of any order. The analysis of elastoplastic defor
mation of elastically anisotropic materials without damage is also pre
sented, with the application to transversely isotropic materials. The
relationships between the elastic and plastic strain rates and the com
ponents of the multiplicative decomposition and their rates are also g
iven.