Recent studies have shown that mechanical stimulation, by means of flow perfusion and mechanical compression (or stretching), enhances osteogenic differentiation of mesenchymal stem cells and bone cells within biomaterial scaffolds in vitro. However, the precise mechanisms by which such stimulation enhances bone regeneration is not yet fully understood. Previous computational studies have sought to characterise the mechanical stimulation on cells within biomaterial scaffolds using either computational fluid dynamics or finite element (FE) approaches. However, the physical environment within a scaffold under perfusion is extremely complex and requires a multiscale and multiphysics approach to study the mechanical stimulation of cells. In this study, we seek to determine the mechanical stimulation of osteoblasts seeded in a biomaterial scaffold under flow perfusion and mechanical compression using multiscale modelling by two-way fluid–structure interaction and FE approaches. The mechanical stimulation, in terms of wall shear stress (WSS) and strain in osteoblasts, is quantified at different locations within the scaffold for cells of different attachment morphologies (attached, bridged). The results show that 75.4 % of scaffold surface has a WSS of 0.1–10 mPa, which indicates the likelihood of bone cell differentiation at these locations. For attached and bridged osteoblasts, the maximum strains are 397 and 177,200 μ ε, respectively. Additionally, the results from mechanical compression show that attached cells are more stimulated (maximumstrain=22,600μ ε) than bridged cells (maximumstrain=10,000μ ε). Such information is important for understanding the biological response of osteoblasts under in vitro stimulation. Finally, a combination of perfusion and compression of a tissue engineering scaffold is suggested for osteogenic differentiation.