A new two-dimensional (2D) material, borophene (2D boron sheet), has been grown successfully recently on single crystal Ag substrates by two parallel experiments [Mannix et al., Science, 2015, 350, 1513] [Feng et al., Nature Chemistry, 2016, advance online publication]. Three main structures have been proposed (β 12 , χ 3 and striped borophene). However, the stability of three structures is still in debate. Using first principles calculations, we examine the dynamical, thermodynamical and mechanical stability of β 12 , χ 3 and striped borophene. Free-standing β 12 and χ 3 borophene is dynamically, thermodynamically, and mechanically stable, while striped borophene is dynamically and thermodynamically unstable due to high stiffness along a direction. The origin of high stiffness and high instability in striped borophene along a direction can both be attributed to strong directional bonding.This work provides a benchmark for examining the relative stability of different structures of borophene.