This paper discusses heterogeneous responses of structures in cases where instability occurs at a microscopic level.Two multiscale approaches are discussed in this respect.Firstly heterogeneous materials are analyzed by the computational homogenization method.The latter combines two levels of continuous models, possibly in a concurrent manner.The discrete version (FE2) combines two meshes at microscopic and macroscopic levels.Such FE2 computations permit to re-discuss microbuckling in long fiber composite materials that is the basic mechanism of failure in compression.