Senescent cells have been recognized to play major roles in tumor progression and are nowadays included in the hallmarks of cancer. Our work aims to develop a mathematical model capable of capturing a pro-invasion effect of senescent fibroblasts located in the conjunctive tissue. We focus in the present article on the first moments of the invasion cascade. Considering a localized epithelial tumor, we model the digestion of the collagen fibers of the basement membrane by the proteolytic enzyme MMP-2. The activation of MMP-2 is modelled in detail, as MT1-MMPs bound to the surface of tumor cells interact with proMMPs and TIMPs, proteins enriched in the secretome of senescent Cancer-Associated Fibroblasts, along with its inhibition by TIMPs. Using numerical simulations of the model, calibrated via an extensive literature search, reproducing biologically relevant scenarios, we test the model’s suitability to investigate the effect on basement membrane digestion of fibroblasts presenting a senescence-associated secretory phenotype. Via model reduction, steady state and global sensitivity analyses, we identify the most influential parameters in view of their calibration with empirical data. We conclude the paper discussing mathematical and interdisciplinary perspectives.