In this paper we construct and analyze a two-well Hamiltonian on 2D atomic lattice considered with nonconvex interactions. Two wells of the Hamiltonian are given by two rank-one connected martensitic twins, respectively. Our combined analytical and numerical results show that the structure of ground states under appropriate boundary conditions is close to the macroscopically expected twinned configuration plus additional exponential boundary layers localized near the twinning interface. Besides, we proceed to continuum limit, show asymptotic piece-wise rigidity of minimizing sequences and derive the limiting form of their surface energy. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)