This paper presents explicit algebraic stress models for three-dimensional turbulent flows in non-inertial frames, derived systematically from a hierarchy of second-order closure models. These models generalize the earlier work of Pope (1975), who derived a two-dimensional model based on the Launder, Reece, and Rodi model. The new models are explicitly related to the Reynolds stress tensor and mean velocity gradients, and they provide a more accurate description of turbulent flows compared to traditional algebraic stress models. The paper also shows that these explicit models can shed new light on the equilibrium states of homogeneous turbulent flows and serve as a useful alternative in practical computations. The paper discusses the theoretical background of turbulent flows, the Reynolds stress transport equation, and the relationship between explicit algebraic stress models and anisotropic eddy viscosity models. It also addresses the need for regularization in algebraic stress models, which is demonstrated through the use of a Padé approximation. The paper then presents the derivation of explicit algebraic stress models for three-dimensional flows, showing that they can be expressed in terms of the mean velocity gradients and other invariants. The paper also compares the new explicit algebraic stress models with other nonlinear Reynolds stress models, showing that they provide a more accurate description of turbulent flows. It presents illustrative examples of the models applied to homogeneous shear flow and fully-developed turbulent channel flow, showing that the new models perform well in capturing the trends of large-eddy simulations and experimental data. The paper concludes that explicit algebraic stress models are a valuable tool for modeling turbulent flows, particularly in complex flows where traditional models fail. These models can be regularized using a Padé approximation, and they provide a more accurate description of turbulent flows than traditional models. The paper also highlights the importance of incorporating rotational strains in the models, which is achieved through the terms $ W^{*} $ and $ \zeta $. The results of this study demonstrate that explicit algebraic stress models can serve as a useful alternative to traditional models in the calculation of complex turbulent flows.This paper presents explicit algebraic stress models for three-dimensional turbulent flows in non-inertial frames, derived systematically from a hierarchy of second-order closure models. These models generalize the earlier work of Pope (1975), who derived a two-dimensional model based on the Launder, Reece, and Rodi model. The new models are explicitly related to the Reynolds stress tensor and mean velocity gradients, and they provide a more accurate description of turbulent flows compared to traditional algebraic stress models. The paper also shows that these explicit models can shed new light on the equilibrium states of homogeneous turbulent flows and serve as a useful alternative in practical computations. The paper discusses the theoretical background of turbulent flows, the Reynolds stress transport equation, and the relationship between explicit algebraic stress models and anisotropic eddy viscosity models. It also addresses the need for regularization in algebraic stress models, which is demonstrated through the use of a Padé approximation. The paper then presents the derivation of explicit algebraic stress models for three-dimensional flows, showing that they can be expressed in terms of the mean velocity gradients and other invariants. The paper also compares the new explicit algebraic stress models with other nonlinear Reynolds stress models, showing that they provide a more accurate description of turbulent flows. It presents illustrative examples of the models applied to homogeneous shear flow and fully-developed turbulent channel flow, showing that the new models perform well in capturing the trends of large-eddy simulations and experimental data. The paper concludes that explicit algebraic stress models are a valuable tool for modeling turbulent flows, particularly in complex flows where traditional models fail. These models can be regularized using a Padé approximation, and they provide a more accurate description of turbulent flows than traditional models. The paper also highlights the importance of incorporating rotational strains in the models, which is achieved through the terms $ W^{*} $ and $ \zeta $. The results of this study demonstrate that explicit algebraic stress models can serve as a useful alternative to traditional models in the calculation of complex turbulent flows.