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In the present study, the effects of rare earth element Y, texture intensity, and grain size on the tension-compression mechanical behavior of extruded Mg-XY(X = 0–3, wt pct) rods were investigated using improved phenomenological crystal plasticity. To this end, finite element modeling of a three-dimensional representative volume element (3D-RVE) was employed to consider the effects of microstructural parameters. Subsequently, the computational modeling approach was validated with the experimental data to assess the reliability of predictions of the responses of a polycrystalline aggregate. Afterward, the validated computational modeling was employed to predict the mechanical behaviors of extruded Mg-XY (X = 0–3, wt pct) by considering the role of slip/twinning activities during deformation. The results showed that the Y addition significantly improved the yield strength, ultimate strength, and ductility. Examination of the deformation modes activities indicated that the basal slip activity of extruded Mg-XY (X = 1–3, wt pct) is higher than that of extruded pure Mg due to the formation of non-basal texture components, which hindered the twinning activation. Increasing the Y content further reduced the suppression of tensile twinning activity. Therefore, the weak tension–compression yield asymmetry of extruded Mg-XY (X = 1–3, wt pct) was mainly attributed to the reduced tensile twinning activity. The simulated stress-strain curves illustrated that texture weakening, and grain refining improved the mechanical behavior and reduced tension-compression yield asymmetry.