Tantalum plate and rod materials that demonstrate mild-to-strong anisotropic plastic flow during large deformation are analyzed in terms of tensorial property symmetry. Texture interrogations of these materials reveal duplex orientation components that have implications with regard to the symmetry realized during plastic deformation; specifically these materials show less symmetry than one would expect from a cursory examination of the texture. Mesoscale polycrystal simulations are performed to probe a general shape for the yield surface function based on a discrete orientation distribution representation of the material texture and previously established single-crystal deformation modes. The yield surface shape is mathematically represented in terms of second and higher-order tensors. A plastic compliance analysis is presented and applied to graphically map the deformation symmetry contained in these tensors for both ideal and real materials. Compliance results are shown to be consistent with finite element simulations of r-value specimens loaded in uniaxial tension.