We report simulations of gas-liquid two-phase flows in microchannels periodically patterned with grooves and ridges. A constant effective body force is applied on both fluids to simulate a pressure-driven creeping flow, and a diffuse-interface model is used to compute the interfacial evolution and the contact line motion. Depending on the body force, capillary force and the level of liquid saturation, a number of flow regimes may appear in the corrugated microchannel: gas flow, blockage, liquid flow, bubble-slug flow, droplet flow, annular flow and annular-droplet flow. A map of flow regimes is constructed for a set of geometric and flow parameters starting from a prescribed initial configuration. Some of the regimes are new, while others have been observed before in straight tubes and pipes. The latter are compared with previous experiments in terms of the regime map and the holdup ratio. The transition among flow regimes shows significant hysteresis, largely owing to the pinning of the interface at sharp corners in the flow conduit. Hysteresis is reduced if the sharp corners are rounded. Under the same operating conditions, different flow regimes can be realized from different initial conditions. The roles of geometry and wettability of the channel walls are also elucidated. (C) 2011 Elsevier Ltd. All rights reserved.