In this talk we present some recent numerical results concerning flows with pressure and shear dependent viscosity. From the numerical point of view several problems arise, first from the difficulty of approximating incompressible velocity fields and, second, from poor conditioning and possible lack of differentiability of the involved nonlinear functions due to the material laws. The lack of differentiability can be treated by regularisation. Then the Newton methods as linearization technique can be applied; moreover the presence of the pressure in the viscosity function leads to an additional term introducing a new non classical linear algebraic saddle point problem. The difficulty related to the approximation of incompressible velocity fields was treated by applying the Rannacher-Turek Stokes element, here also we were facing another problem related to the nonconforming approximation for problems involving the symmetric part of gradient. In fact, the classical discrete Korn`s Inequality is out of being satisfied. A new and more general approach which involves the jump across the interelement boundaries should be used, which means a small modification of the discrete bilinear form by adding an interface term, penalizing the jump of the velocity. This is a modified procedure in the derivation of Discontinuous Galerkin formulation. A Vanka smoother as defect correction inside of a direct multigrid approach is presented. The results of some computational experiments for realistic flow configurations are provided, which contain a pressure dependent viscosity, too. In particular we present results for modelling granular flow via the ``Schaeffer model``.