A special theory of elastic-plastic response is considered in which the internal energy density, free energy density, entropy density, and Cauchy stress are taken to be functions of elastic deformation gradient, plastic deformation gradient, and temperature. The minimum symmetries of the elastic response are evaluated. It is shown that the minimum symmetries of the elastic response can be obtained from the material's initial symmetries and the value of the plastic deformation gradient. It is also shown that symmetries of the elastic response can not be reduced by plastic deformation in non-thermodynamic theories which take the stress to only be a function of elastic deformation gradient and temperature, or for thermodynamic theories for which the free energy is assumed to only be a function of elastic deformation gradient and temperature. Therefore, in these special cases, if a material is initially isotropic, its elastic response will remain isotropic; if the material is initially transversely isotropic, its elastic response will remain transversely isotropic; etc.