This article presents a new explicit algebraic Reynolds stress model for wall-bounded turbulent flows, developed within the elliptic blending strategy framework. The main objective is to drastically reduce the model’s nonlinearity while properly capturing near-wall effects for the normal components of the anisotropy tensor. Algebraic models are based on the weak-equilibrium assumption, according to which the advection and diffusion of the anisotropy tensor can be neglected. Although these models avoid solving transport equations for the Reynolds stresses, the nonlinearities induced by classical closures make their solution as complex as that of second-order models. The elliptic blending strategy (see e.g. [2]) allows expressing the difference between pressure redistribution and dissipation as a linear combination of a near-wall contribution and a homogeneous model valid far from the wall. A coefficient α, solution of an elliptic equation, ensures the transition between these two regions. For two-dimensional mean flows, a simple algebraic relation is derived in the present study, similar to that proposed by Girimaji [1]. This relation is then extended to three-dimensional flows through an approximation that resembles existing near-wall modifications [3]. The model is assessed a priori on a turbulent channel flow at Reτ = 550 using DNS data. The results show that the model correctly reproduces the two-component limit of turbulence near the wall, where the normal component is significantly weaker than the streamwise and spanwise components. Despite its simplicity, a priori evaluation shows that both the two-component limit and the wall shear stress are correctly reproduced.