[en] Well-known Kato’s theory of the Laue diffraction of spherical X-ray waves is generalized to the case of the neutron diffraction in strongly absorbing crystals, taking into consideration both the potential and the resonant scattering of neutrons by nuclei as well as a realistic angular dispersion of incident neutrons. The saddle-point method is applied for estimation of the angular integrals, being more adequate in the case of strongly absorbing crystals than the commonly used stationary-phase approximation. It is found that the intensity distribution of the diffracted and refracted beams along the basis of the Borrmann triangle significantly depends on the deviation of the neutron energy from the nuclear resonant level. When comparing our calculations with the Shull’s experimental data on neutron diffraction in silicon, we also regard the role of finite width of the collimating and scanning slits.