The aim of this paper is a priori evaluation and improvement of an explicit algebraic Reynolds stress model (EASM) which has been devised by Shih et al. (1995). This model which accounts for anisotropy is used to compute the turbulent flow through a square duct. It is based on a quadratic stress-strain relation which is obtained by applying the constraint of rapid distortion theory and the realizability constraint. The Reynolds number based on the averaged velocity and on the height of the duct is 4800. hi order to handle wall-proximity effects in the near-wall region, damping functions are implemented in the ShihM. Direct numerical simulation (DNS) of the Navier-Stokes equations is available for this case. The comparison of the ShihM results with these accurate simulations shows good agreements. The aspects of the state of such turbulent flow is summarized by the map of the second and third invariants of the Reynolds stress tensor.