While cyclic adenosine monophosphate (cAMP) is typically considered an intracellular signal, it has been shown to spread between adjacent cells through connexin-based gap junction channels, promoting gap junctional intercellular communication (GJIC). Gap junction-mediated signaling is critical for the coordinated function of many tissues, and have been linked with cardiovascular disease, neurogenerative disease, and cancers. In particular, it plays a complex role in tumor suppression or promotion. This work introduces a two-dimensional finite element model that can describe intercellular cAMP signaling in the presence of gap junctions on membrane interfaces. The model was utilized to simulate cAMP transfer through one and two gap junction channels on the interface of a cluster of two pulmonary microvascular endothelial cells. The simulation results were found to generally agree with what has been observed in the literature in terms of GJIC. The research outcomes suggest that the proposed model can be employed to evaluate the permeability properties of a gap junction channel if its cAMP volumetric flow rate can be experimentally measured.