In this thesis we provide an existence result for a regularized model of viscoelastic non- newtonian fluid. We consider incompressible fluid with shear rate dependent viscosity and with Cauchy stress tensor capable to describe stress relaxation. An elastic part of the Cauchy stress tensor is governed by Oldroyd-type differential equation. In particular, we are interested in fluids with strong shear thinning effect. We prove that if the viscosity function µ (D) is such that tensor µ (D) D is p-coercive, monotone and has (p − 1)-growth for p > 6 5 and some other additional assumptions are satisfied, then there exists a solution to the system of PDEs describing the flow in a bounded domain. The proof is not simple because the convective term is not integrable with a high power. The problem is solved using Lipschitz truncation method for evolution PDEs. 1