Mast cells (MCs) play an important role in the immune system. Through connective tissues, mechanical stimuli activate intracellular calcium signaling pathways, induce a variety of mediators including leukotriene C$_4$(LTC$_4$) release, and affect MCs' microenvironment. This paper focuses on MCs' intracellular calcium dynamics and LTC$_4$ release responding to mechanical stimuli, explores signaling pathways in MCs and the effect of interstitial fluid flow on the transport of biological messengers and feedback in the MCs network. We use a mathematical model to show that (i) mechanical stimuli including shear stress induced by interstitial fluid flow can activate mechano-sensitive (MS) ion channels on MCs' membrane and allow Ca$^{2+}$ entry, which increases intracellular Ca$^{2+}$ concentration and leads to LTC$_4$ release; (ii) LTC$_4$ in the extracellular space (ECS) acts on surface cysteinyl leukotriene receptors (LTC$_4$R) on adjacent cells, leading to Ca$^{2+}$ influx through Ca$_{2+}$ release-activated Ca$^{2+}$ (CRAC) channels. An elevated intracellular Ca$^{2+}$ concentration further stimulates LTC$_4$ release and creates a positive feedback in the MCs network. The findings of this study may facilitate our understanding of the mechanotransduction process in MCs induced by mechanical stimuli, contribute to understanding of interstitial flow-related mechanobiology in MCs network, and provide a methodology for quantitatively analyzing physical treatment methods including acupuncture and massage in traditional Chinese medicine (TCM).