Graphene-like two dimensional (2D) monolayers composed of β-structured Group 15 (β-G15) elements have attracted great attention due to their intrinsic bandgaps, thermodynamic stabilities and high mobilities. Quite different from graphene, a buckle with amplitude ranging from 1.24 Å to 1.65 Å exists along the z direction in β-G15 films. To learn the growth behaviours and the relevant influence of such buckles, here, we performed a systematic study on the edge stabilities of monolayer films constructed with β-phase P, As, Sb and Bi, respectively. Our theoretical results show that, for free-standing films, the zigzag edge with dangling atoms is the most stable one for bare P, As and Sb and the pristine AC edge is the most stable one for Bi, while the pristine zigzag edge becomes the most stable one for all films if the edge is terminated with hydrogen atoms, both resulting in hexagonal flakes under equilibrium growth conditions. Buckles show no apparent influence on the edge stabilities in free-standing films while play a significant role in cases considering underlying metal substrates. Such an influence can be attributed to the charge transfer difference between the lower/upper β-G15 atoms and underlying substrates, which may eventually determine the growth mechanism and morphologies of 2D β-G15 films. Detailed growth kinetics and properties were also discussed based on the first-principles results. The understanding of these fundamental principles should provide useful information for guiding the synthesis of β-G15 films and other 2D materials.