  In this paper, some properties of resonances for multi-dimensional quantum
walks are studied. Resonances for quantum walks are defined as eigenvalues of
complex translated time evolution operators in the pseudo momentum space. For
some typical cases, we show some results of existence or nonexistence of
resonances. One is a perturbation of an elastic scattering of a quantum walk
which is an analogue of classical mechanics. Another one is a shape resonance
model which is a perturbation of a quantum walk with a non-penetrable barrier.
