We have significantly improved a method to characterize the displacement fields near edge dislocations in ordered polymers. Our extended analysis now makes it possible to predict and explain the variation in tilt of different lattice planes in the vicinity of dislocations in isotropic solids, anisotropic crystals, and liquid crystals in terms of their elasticity constants. Direct images of the dislocation cores were obtained in three different polymer systems using bright field transmission electron microscopy (TEM) and high-resolution electron microscopy (HREM). A b[010] = 63 nm edge dislocation was imaged in the ABC triblock copolymer polystyrene-block -poly(ethylene-co -butylene) -block -poly(methyl methacrylate) (SEBM). The isotropic displacement fields according to theories by Taylor and Burgers were compared to the SEBM data. Fitting the theoretical displacement fields to the displacements measured from the image, an estimate of the elastic constant anisotropy was obtained. For this material the ratio of the bulk modulus to the shear modulus, K/G, was equal to 0.8 +/-0.2. A similar analysis using anisotropic dislocation theory was applied to a three chain-end, b[200] 2.4 nm edge dislocation in the crystalline polymer [1,6-di(N-carbazolyl)-2,4-hexadiyne] (DCHD). Information about the anisotropy of DCHDs stiffness matrix, C-ij, was obtained. An anisotropy parameter W-2, defined as (C-11 + C-33)/(2C(55)), was found to be 3.0 +/- 0.1. Finally, a b = 2.6 nm dislocation in a smectic polymalonate was analyzed using liquid crystalline dislocation theory. An estimate of lambda, the material's characteristic deformation length, was determined to be 1.1 +/- 0.1 nm.