Structural, electronic, intrinsic magnetic, anisotropic elastic properties, sound velocities and Debye temperature of Fe1−xMnx B (x = 0, 0.25, 0.5, 0.75, 1) transition metal monoborides have been studied by first-principles calculations within the method of virtual crystal approximation (VCA) based on density-functional theory (DFT) through generalized gradient approximation (GGA). The average magnetic moment per cell increased with increasing of Mn content, which could be associated with the relationship between the composition and magnetic properties. The observed magnetic behavior of Fe1−xMnx B compounds can be explained by Stoner model. Lattice parameters and Debye temperature agree well with the experimental values. Furthermore, we have plotted three-dimensional (3D) surfaces and planar contours of the directional dependent Young and bulk moduli of the compounds on several crystallographic planes, to reveal their elastic anisotropy versus Mn content (x) in Fe1−xMnx B.