Summary: For the model of a viscous incompressible fluid, where the viscous stress tensor satisfies the growth condition \(|\tau_{ij}(e)|\leq C\bigl(1+| e|\bigr)^{p-1}\), with \(e\) the rate of strain tensor, we prove the existence of Young measure valued solutions for \(p>1\) if \(n=2\), and for \(p>6/5\) if \(n=3\), the existence of weak solutions for \(p>3/2\) if \(n=2\), and for \(p>9/5\) if \(n=3\), and the existence of unique regular weak solutions for \(p\geq 2\) if \(n=2\), and for \(p\geq 11/5\) if \(n=3\). The analysis deals with the associated space periodic problem.