In most of partially averaged Navier-Stokes (PANS) methods, the Reynolds stress is solved by a linear hypothesis isotropic model. They could not capture all kinds of vortexes in tubomachineries. In this paper, a PANS model is modified from the RNG k -ε turbulence model and is used to investigate the influence of the nonlinear shear stress on the simulation of the high pressure gradient flows and the large curvature flows. Comparisons are made between the result obtained by using the PANS model modified from the RNG k -ε model and that obtained by using the nonlinear PANS methods. The flow past a curved rectangular duct is calculated by using the PANS methods. The obtained nonlinear shear stress agrees well with the experimental results, especially in the high pressure gradient region. The calculation results show that the nonlinear PANS methods are more reliable than the linear PANS methods for the high pressure gradient flows, the large curvature flows, and they can be used to capture complex vortexes in a turbomachinary.