We present a new approach to the numerical solution of Takagi equations, based on the Finite Element Method (FEM) that starting from a weak formulation of differential equations is much more versatile than the usual Finite Difference method (FDM). In particular, this is the only available approach that can easily handle with calculation where the free space propagation is required, as in the case of focusing by curved crystals, but also some crystals cut with special geometries that are useful for neutron monochromators.