  Scattering of a time harmonic anti-plane shear wave due to either a pair of
crack tips or a pair of rigid constraint tips on square lattice is considered.
The two problems correspond to the so called zero-offset case of scattering due
to a pair of identical Sommerfeld screens. The peculiar structural symmetry
allows the reduction of coupled equations to two scalar Wiener-Hopf equations
and a total of four geometrically reduced problems on lattice half-plane. Exact
solution of each problem for incidence from the bulk lattice, as well as from
an associated lattice waveguide, is constructed. A suitable superposition of
the four expressions is used to construct the solution of the main problem. The
discrete paradigm involving the wave mode incident from the waveguide is
relevant for modern applications where an investigation of mechanisms of
electronic and thermal transport at nanoscale remains an interesting problem.
