In this paper, the problem of finite-region stability is studied for a class of two-dimensional (2-D) singular systems described by using the Roesser model with directional delays. Based on the regularity, we first decompose the underlying singular 2-D systems into fast and slow subsystems corresponding to dynamic and algebraic parts. Then, with the Lyapunov-like 2-D functional method, we construct a weighted 2-D functional candidate and utilize zero-type free matrix equations to derive delay-dependent stability conditions in terms of linear matrix inequalities (LMIs). More specifically, the derived conditions ensure that all state trajectories of the system do not exceed a prescribed threshold over a pre-specified finite region of time for any initial state sequences when energy-norms of dynamic parts do not exceed given bounds
