The study of how mechanical interactions and different cellular behaviors affect tissues and embryo shaping has been and remains an important challenge in biology. Axial extension is a morphogenetic process that results in the acquisition of the elongated shape of the vertebrate embryonic body. Several adjacent tissues are involved in the process, including the tissues that form the spinal cord and musculoskeletal system: the neural tube and the paraxial mesoderm, respectively. Although we have a growing understanding of how each of these tissues elongates, we still need to fully understand the morphogenetic consequences of their growth and mechanical interactions. In this study, we develop a 2D multi-tissue continuum-based mathematical model to simulate and study how differential growth, tissue biophysical properties, and mechanical interactions affect the morphogenesis of the embryonic body during axial extension. Our model captures the long-term dynamics of embryonic posterior tissues previously observed in vivo by time-lapse imaging of bird embryos. It reveals the underestimated influence of differential tissue proliferation rates in inter-tissue interaction and shaping by capturing the relative impact of this process on tissue dynamics. We verified the predictions of our model in quail embryos by showing that decreasing the rate of cell proliferation in the paraxial mesoderm affects long-term tissue dynamics and shaping of both the paraxial mesoderm and the neighboring neural tube. Overall, our work provides a new theoretical platform to consider the long-term consequences of tissue differential growth and mechanical interactions on morphogenesis.