The behaviour of soft tissues is heavily influenced by their mechanical microenvironment. Mechanical forces have been shown to play a crucial role in the development of cells and tissues. However, the impact of mechanical interactions on tissue behaviours is made more complex since tissues can generate forces through growth and cellular contractility. In this thesis, we develop continuum mechanics models based on the theory of elasticity to understand the mechanical behaviour of organoid experiments.

We first consider an active stress approach to model cellular contractility on the tissue level. With a linear elastic framework and symmetry arguments, analytical solutions for the deformations can be found. We show that the ratio of tissue stiffness and matrix stiffness is a key parameter for the existence of potential mechanical signalling mechanisms. We further develop this model to account for mechanical feedback, in which the contractile response of the tissues now depends on its strain. With this feedback mechanism, we show an effective stiffening of the tissue. The tissue's Poisson ratio plays a pivotal role in driving this stiffening phenomenon, underscoring the significance of tissue compressibility. We find that the predicted response of tissues in 3D differs greatly from the response of cells in 2D experiments.

We then introduce a framework for modelling tissue growth using elasticity theory, switching to a nonlinear framework in doing so. We further highlight the importance of the relative stiffness between the tissue and the surrounding matrix. We develop our framework further by coupling contractility into the growth model. We find that growth and contractility are in some sense antagonistic mechanics, where they oppose the deformations caused by each other. Finally, we consider possible mechanisms for stress-based growth which further highlight the importance of tissue compressibility on the mechanical behaviour of organoids.