An approach is described to compute extremely asymmetric X-ray diffraction in multilayers and superlattices taking account of the normal lattice strain. This method is based on the dynamical theory of X-ray diffraction and on a matrix form of boundary conditions, thus providing a simple numerical solution to the problem. The developed approach can be used to interpret extremely asymmetric X-ray diffraction measurements of lattice strains in semiconductor multilayers and in other surface structures.