Cells, tissues and organs function in a three-dimensional (3D) environment. Ideally, cell-based models that capture both the 3D organization and multi-cellular complexity of the native system provide the most powerful tools for screening the effects of therapeutic candidates. This approach to drug discovery bridges tissue engineers, who are constructing 3D tissues, with biologists, who are studying healthy versus diseased states and to pharmacologists, who are developing screening assays. Within this context, an innovative biophysical perspective of tissue morphogenesis, malignancy and treatment responsiveness has been established recently. Numerous experimental studies have shown that mechanical loading regulates the anabolic and catabolic metabolism of cells. Anabolic mechanisms, in particular, are of vital importance in the process of tissue engineering, which is of increasing scientific and clinical interest. Cells seeded and cultured in appropriate constructs should be mechanically stimulated to produce and to structure the required constituents of the extracellular matrix. However, the determination of the most effective type of loading, the appropriate load history and the mechanical field variables responsible for the stimulation of the cell activity, as well as the pathways of communication among cells, are still subject of contrary discussions and motivation of recent investigation. In this review we discuss the tissue-level response to mechanical signalling, we provide an overview of prominent techniques currently used for exerting mechanical stresses on engineered tissue and an overview of numerical mechanics studies providing information on mechanical field variables potentially triggering the biological activity.