  Various models of tumor growth are available in the litterature. A first
class describes the evolution of the cell number density when considered as a
continuous visco-elastic material with growth. A second class, describes the
tumor as a set and rules for the free boundary are given related to the
classical Hele-Shaw model of fluid dynamics. Following the lines of previous
papers where the material is described by a purely elastic material, or when
active cell motion is included, we make the link between the two levels of
description considering the 'stiff pressure law' limit. Even though viscosity
is a regularizing effect, new mathematical difficulties arise in the
visco-elastic case because estimates on the pressure field are weaker and do
not imply immediately compactness. For instance, traveling wave solutions and
numerical simulations show that the pressure may be discontinous in space which
is not the case for the elastic case.
