The capillary valve effect is studied on the capillary force dominated immiscible two-phase flows in the networks composed of regular pores and throats. Two types of pore invasion are revealed. One is bursting invasion, where the invading fluid enters a pore from one throat. The other is merging invasion, where a pore is invaded by the invading fluid from two throats. Drainage and imbibition are similar and show capillary fingering pattern in the cases where bursting invasion dominates over merging invasion. When merging invasion is dominant, a stable flow pattern can also be observed. (C) 2015 Elsevier Ltd. All rights reserved.