  In this paper, we study tropicalisations of singular surfaces in toric
threefolds. We completely classify singular tropical surfaces of
maximal-dimensional type, show that they can generically have only finitely
many singular points, and describe all possible locations of singular points.
More precisely, we show that singular points must be either vertices, or
generalized midpoints and baricenters of certain faces of singular tropical
surfaces, and, in some cases, there may be additional metric restrictions to
faces of singular tropical surfaces.
