The uncontrolled growth of tumor tissue often results from the combined effects of mutations to tumor suppressor and oncogenes. Gastrointestinal tumors are influenced by stimulation and inhibition from the interleukin-6/11 (IL-6/11) and transforming growth factor-β (TGF-β) systems. This study aims to analyse the interactions between these two signalling systems in epithelial cells, determine the levels of critical signalling components and establish dynamic models to stimulate the crosstalk and outputs from both signalling pathways. Oncogenic and/or tumor suppressor mutations are modeled with a view to identifying targets for interfering with the growth of stomach or colon cancers. This work focuses on the initial stages in the TGF-β and IL-6/11 signalling pathways separately. Mathematical modeling of the signalling pathways as a novel method in computational and systems biology is recruited in this study. The separated models can be then used to introduce an integrated model based on their interactions. The integrated model establishes the first step in understanding cancer and its causes.