Big mechanically-active culture systems (BigMACS) are promising to stimulate, control, and pattern cell and tissue behaviours with less soluble factor requirements. However, it remains challenging to predict if and how distributed mechanical forces impact single-cell behaviours to pattern tissue. In this study, we introduce a tissue-scale finite element analysis framework able to correlate sub-cellular quantitative histology with centimetre-scale biomechanics. Our framework is relevant to diverse BigMACS, including media perfusion, tensile-stress, magnetic, and pneumatic tissue culture platforms. We apply our framework to understand how the design and operation of a multi-axial soft robotic bioreactor can spatially control mesenchymal stem cell (MSC) proliferation, orientation, differentiation to smooth muscle, and extracellular vascular matrix deposition. We find MSC proliferation and matrix deposition to positively correlate with mechanical stimulation but cannot be locally patterned by soft robot mechanical stimulation within a centimetre scale tissue. In contrast, local stress distribution was able to locally pattern MSC orientation and differentiation to smooth muscle phenotypes, where MSCs aligned perpendicular to principal stress direction and expressed increased α-SMA with increasing 3D Von Mises Stresses from 0 to 15 kPa. Altogether, our new biomechanical-histological simulation framework is a promising technique to derive the future mechanical design equations to control cell behaviours and engineer patterned tissue.