The equations for calculating diffraction profiles for bent crystals are revisited for both meridional and sagittal bending. Two approximated methods for computing diffraction profiles are treated: multilamellar and Penning-Polder. A common treatment of crystal anisotropy is included in these models. The formulation presented is implemented into the XOP package, completing and updating the crystal module that simulates diffraction profiles for perfect, mosaic and now distorted crystals by elastic bending.