The computational formulation of a new nonequilibrium Reynolds stress closure is presented along with preliminary validation results for both homogeneous and inhomogeneous turbulent flow problems of practical engineering importance. The new nonequilibrium closure, which has been rigorously derived elsewhere,1replaces the classical Boussinesq hypothesis appearing in many current two-equation turbulence models with a comparably simple representation for the Reynolds stresses, thereby allowing straightforward implementation in existing computational frameworks. The new nonequilibrium closure has been extended to include a rigorously derived realizable eddy viscosity, and theoretical details of the closure are evaluated through fundamental tests of periodically and impulsively sheared homogeneous turbulence. The full computational formulation of the nonequilibrium closure is outlined for both k-ω and k-ω model frameworks. Finally, preliminary inhomogeneous flow results are presented using the k-ω framework for turbulent flow over a flat-plate and the interaction of an impinging oblique shock wave with a turbulent boundary layer.