This paper analyzes the decomposition of finite deformation into elastic an
d plastic parts. The analysis argues that Lee's multiplicative decompositio
n of the deformation gradient is not the real separation of the total defor
mation into elastic and plastic parts and that the Green strain cannot be d
ecomposed into elastic and plastic parts. The paper also analyzes the decom
position of the velocity gradient and presents an exact elastic-plastic dec
omposition of deformation rate.