  We study a free boundary problem modelling the growth of non-necrotic tumors
with fluid-like tissues. The fluid velocity satisfies Stokes equations with a
source determined by the proliferation rate of tumor cells which depends on the
concentration of nutrients, subject to a boundary condition with stress tensor
effected by surface tension. It is easy to prove that this problem has a unique
radially symmetric stationary solution. By using a functional approach, we
prove that there exists a threshold value $\gamma_*>0$ for the surface tension
coefficient $\gamma$, such that in the case $\gamma>\gamma_*$ this radially
symmetric stationary solution is asymptotically stable under small non-radial
perturbations, whereas in the opposite case it is unstable.
