  The mechanical properties of tissues play an essential role for all tissue
properties such as cell division, and differentiation or morphogenesis. Here,
we study theoretically the rheology of 2-dimensional epithelial tissues
described by a discrete vertex-like model, using an analytical coarsegrained
continuum formulation. We show that epithelial tissues are most often
shear-thinning under constant shear rate, and in certain circumstances cross
over from shear thickening at low shear rates to shear thinning at high shear
rates. We give an analytical expression of the tissue response in an
oscillating strain experiment in the linear regime, and calculate it
numerically in the non-linear regime. When the tissue is supported by an
oscillating substrate, it reorients depending on frequency and substrate's
Poisson's ratio. Reorientation could be gradual or abrupt, depending on tissue
and substrate parameters, and the configuration phase space exhibits a
tricritical point.
