A large portion of oil and gas reservoirs in the world are located in naturally fractured reservoirs. Despite such importunity, the production mechanisms of these reservoirs are not completely well defined. Gas-oil gravity drainage that takes place in the gas-invaded zone of this type of reservoirs is one instance of such a weakness. The density difference between gas-filled fractures in contact with oil-saturated matrix blocks brings the oil out of the matrix blocks into the fracture. The drained oil can reach the production well through two different paths: continues fracture network and block-to-block path. These two different paths require different approaches to modeling of gravity drainage. Single-block approaches are used when drained oil only travels through the fracture network, which totally formulated before. But when oil prefers to travel through the matrix blocks, continuum approaches such as Darcy's law may not work in their basic forms any more. Liquid bridges and film that form in the horizontal fracture between matrix blocks usually transfer the wetting phase across the fracture. Stability condition and duration of stability can help better understanding of gravity drainage in stacks of blocks. In this article, the stability of liquid bridges between the matrix blocks studied and a minimum length of stability is predicated. The results show that this stable length of liquid bridges formed between adjacent matrix blocks is 2r0π, which is a function of the pore throat. This critical length can be used in modeling of capillary continuity and wetting phase transfer across matrix blocks.