In this paper we investigate the magnetostrictive [(3/2)λ100 and (3/2)λ111] and elastic (c′ and c44) behavior of single crystalline alloys Fe100-xMox for 2<x<12; the magnetoelastic coupling constants (-b1 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- - 032; 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.