Adaptive wall functions for the Low-Reynolds Number second moment closure turbulence model (EB-RSM for Elliptic Blending Reynolds Stress Model) have been derived in the present work to be used in industrial configurations for incompressible flows. The wall functions are implemented through the use of an algebraic system of equations for the Reynolds Stresses and of blended analytical laws for other quantities. On fine grids (y+ <1), the approach yields results consistent with an integrated solution to the wall. On coarse grids (y+ >30) the results are those of a High-Reynolds Number turbulence model whereas, with intermediate refinements, the results are not deteriorated, which is not the case of standard approaches. Moreover, non equilibrium effects due to pressure gradient are introduced in the wall functions. Detailed numerical results obtained on a 1D and 2D Channel Flows with various refinements and on a backward facing step with a mesh representative of an industrial refinement are presented.