  A mathematical model for tissue growth is considered. This model describes
the dynamics of the density of cells due to pressure forces and proliferation.
It is known that such cell population model converges at the incompressible
limit towards a Hele-Shaw type free boundary problem. The novelty of this work
is to impose a non-overlapping constraint. This constraint is important to be
satisfied in many applications. One way to guarantee this non-overlapping
constraint is to choose a singular pressure law. The aim of this paper is to
prove that, although the pressure law has a singularity, the incompressible
limit leads to the same Hele-Shaw free boundary problem.
