The elastic properties of ferromagnetic Fe1-x-yMnyAlx (0 <= x <= 0.5, y = 0, 0.1, and 0.2) random solid solutions in the body-centered cubic (bcc) crystallographic phase have been investigated using the ab initio exact muffin-tin orbitals method in combination with the coherent-potential approximation. Comparison with the experimental data demonstrates that the employed theoretical approach accurately captures the observed composition dependence of the lattice parameter. The predicted elastic parameters follow complex composition dependence. The C-11, C-12, and C' = (C-11 - C-12)/2 single-crystal elastic constants, the bulk (B), shear (G), and Young's (E) moduli, and the Cauchy pressure (C-12 - C-44) mainly decrease with increasing Al content, whereas the Zener anisotropy ratio (C-44/C') strongly increases with x. C-44 exhibits a non-linear x dependence. The Poisson (v) and Pugh (B/G) ratios first decrease with x but show non-monotonous behavior in high-Al alloys. In terms of the Pugh criterion, these trends suggest an increased brittleness in Al-containing alloys. Manganese has a complex non-monotonous effect on B/G in low-Al alloys (below similar to 15 at. % Al) but enhances the brittleness of the bcc solid solution in large-Al regime. The peculiar Mn alloying effect is explained in terms of magneto-volume mechanisms. (C) 2015 AIP Publishing LLC.