Elastic-modulus mismatch and the resultant stress partitioning in two-phase Mg–Zn–Y alloys comprised of α-Mg and long-period stacking ordered (LPSO) phases were studied. Two-phase polycrystals containing anisotropically oriented 18R- or 14H-type LPSO phase and single-phase polycrystals consisting of α-Mg or 18R-type LPSO phase were prepared by extrusion and directional solidification processes and their complete sets of anisotropic elastic properties were measured using resonant ultrasound spectroscopy. Elastic properties of the single and two-phase alloys were analyzed using Eshelby's inclusion theory, effective-medium approximation, and inverse Voigt-Reuss-Hill approximation, in which the crystallographic textures and microstructures formed by the preparation processes were taken into account. The analyses revealed that the elastic properties of 18R-LPSO phase were not unique and they depended on the solute Zn and Y atom concentrations. Additionally, the elastic modulus of 18R-LPSO phase embedded in the two-phase alloy was lower than that of the alloy consisting of single-phase 18R-LPSO phase. The analysis using first-principles calculations based on density functional theory indicated that the low elastic modulus was caused by low density and low stability of short-range ordered solute atom clusters embedded in the LPSO phase of the two-phase alloy. Because of low elastic modulus in the LPSO phase, the elastic mismatch and resultant elastic interaction between the α-Mg and LPSO phases were very small. As a result, the formation of LPSO phase had little effect on the stress partitioning to the LPSO phase, which was independent of the LPSO-phase morphology.