In this paper we investigate the magnetostrictive [(3/2)λ₁₀₀ and (3/2)λ₁₁₁] and elastic (c′and c₄₄) behavior of single crystalline alloys Fe_100−xMo_x for 21 and −b₂) are computed from the measurements. Similar to other Fe–X (X = Al, Ga, and Ge) alloys, the tetragonal magnetostriction (3/2)λ₁₀₀ increases monotonically from ∼ 70×10⁻⁶ at ∼ 2.5 at. % Mo to a maximum of either ∼ 100×10⁻⁶ at ∼ 8 at. % Mo for the slow cooled crystals or ∼ 125×10⁻⁶ at ∼ 11 at. % Mo for quenched crystals. A sharp decrease after the peak is observed for the slow cooled crystals due to the formation of a second phase. The rhombohedral magnetostriction (3/2)λ₁₁₁ of the Fe–Mo alloys is found to be insensitive to the Mo content. This behavior is distinctly different from other Fe–X (X = Al, Ga, and Ge) alloys where a slight decrease in magnitude and a sign reversal upon chemical ordering was observed for (3/2)λ₁₁₁. Both shear elastic constants (c′ and c₄₄) for Fe–Mo are remarkably insensitive to the Mo content, which is also distinct from the other Fe-based alloys used in the comparison. The two magnetoelastic coupling constants −b₁ = 3λ₁₀₀c′ (with values from 7.15 to 9.77 MJ/m³) and −b₂ = 3λ₁₁₁c₄₄ (with values from −4.96 to −5.81 MJ/m³) were calculated and compared with those of other Fe–X (X = Al, Ga, and Ge) alloys.