We present a mechanical model to describe the growth of healthy and cancerous tissues.
We first show that because of the coupling between cell division and the local stress, a tissue can be considered as a visco-elastic liquid with a relaxation time smaller than the cell division time. We propose a two fluid-model taking into account the interstitial fluid between the cells. We then discuss various instabilities of epithelial tissues that can be of physicological relevance :
-villis are the protrusions of the surface of the intestine or the colon. We describe the formation of villis as a buckling instability of a polar cell monolayer. The polarity of the layer does not seem to play a role in the intestine where the villis are arranged in a square array but it is important in the colon where they are organized in a hexagonal array.
-tubular tissue structures such as arteries or the renal excretory canals show various instabilities also related to buckling
-thick epithelia have a fingering instability of their basement membrane