Mechanical feedback has been identified as a key regulator of tissue growth, by which external signals are transduced into a complex intracellular molecular machinery. Using multiscale computational modeling of multicellular growth in two largely different experimental settings with the same cell line we demonstrate that the cellular growth response on external mechanical stress may nevertheless be surprisingly quantitatively predictable. Our computational model represents each cell as an individual unit capable of migration, growth, division, and death and is parameterized by measurable biophysical and bio-kinetic parameters. A cell cycle progression function depending on volumetric cell compression is established by from comparisons of computer simulations with experiments of spheroids growing in an alginate elastic capsule. After an intermediate calibration step with free growing spheroids growing in a liquid suspension to capture the different growth conditions, the model using the same cell cycle progression function can predict the mechanical stress response of spheroid growth in another experimental technique using Dextran, where stress is exerted by osmotic pressure, even though the experimental results appear differently in both experiments. Our findings suggest that the stress response of cell growth may be highly reproducible even in otherwise different environments. This encourages that robust functional modules may be identified that help us to understand complex cell behavior such as cell growth and division in relation to mechanical stress. The model analysis further elucidates the relation between applied pressure, cell compressibility and cell density. Moreover, the model developments within this paper points a way of how to handle the so far open issue of high compression within the popular so-called " Center-Based Models " , in which force between cells a modelled as forces between cell centers.