  We construct new examples of self-translating surfaces for the mean curvature
flow from a periodic configuration with finitely many grim reaper cylinders in
each period. Because this work is an extension of the author's article on the
desingularization of a finite family of grim reaper cylinders, we simply
discuss the ideas of the construction and here prove only that the periodic
configuration has the necessary flexibility. These examples show that
self-translating surfaces do not necessarily have quadratic volume growth rate
in contrast to self-shrinking surfaces.
