The resonance scattering transfer cross section has been reformulated to account for anisotropic scattering in the center of mass of the neutron-nucleus system. The main innovation over previous implementations is the relaxation of the ubiquitous assumption of isotropic scattering in the center of mass and the actual effective use of scattering angle distributions from evaluated nuclear data files in the computation of the angular moments of the resonant scattering kernels. The formulas for the high-order anisotropic moments in the laboratory system are also derived. A multigroup numerical formulation is derived and implemented into a module incorporated within the NJOY nuclear data processing code. An ultrafine-energy-mesh cross-section library was generated using these new theoretical models and then was used for fuel assembly calculations with the PARAGON lattice physics code. The results obtained indicate that this new model makes a significant difference to predictions of reactivity, multigroup fluxes, and isotopic inventory during depletion.