The performance of a nonlinear k-ϵ turbulence closure model (NKEM), in the prediction of isothermal incompressible turbulent flows, is compared with that of the stress transport models such as the differential Reynolds stress transport model (RSTM) and the algebraic stress transport model (ASTM). Fully developed turbulent pipe flow and confined turbulent swirling flow with a central non-swirling jet are numerically predicted using the Marker and Cell (MAC) finite difference method. Comparison of the prediction with the experiment show that all three models perform reasonably well for the pipe flow problem. For the swirling flow problem, the RSTM and ASTM is superior than the NKEM. RSTM and ASTM provide good agreement with measured mean velocity profiles. However, the turbulent stresses are over- or under-predicted. NKEM performs badly in prediction of mean velocity as well as the turbulent stresses.