An improved algebraic Reynolds stress model is developed from the modeled dynamic equations for the Reynolds stress. The improved model more closely represents the original Reynolds stress model equation than the standard algebraic Reynolds stress model over the range of time scales for the turbulence and mean flow strain field. Quasi-non-local convective effects are also included in the formulation. Explicit solutions to the algebraic Reynolds stress model equation set, in the form of nonlinear stress-strain models, are presented for two and three dimensions.