The elastic properties of edges are among the most fundamental properties of finite two-dimensional (2D) crystals. Using a combination of the first-principles density functional theory calculations and a continuum elasticity model, we present an efficient technique to determine the edge stresses of non-stoichiometric orientations in multicomponent 2D crystals. Using BN and MoS2 as prototypical examples of 2D binary monolayers with threefold in-plane symmetry, we unambiguously compute unique edge stresses of commonly observed non-stoichiometric edges. Our results show that the edge stresses for these structurally distinct orientations can differ significantly from the average values that have been typically reported to date.