Oriented block copolymers exhibit a buckling instability when submitted to a tensile test perpendicular to the lamellae direction. In this paper we study this behavior using a coarse grained molecular dynamics simulation approach. Coarse grained models of lamellar copolymers with alternate glassy rubbery layers are generated using the radical like polymerization method, and their mechanical response is studied. For large enough systems, uniaxial tensile tests perpendicular to the direction of the lamellae reveal the occurrence of the buckling instability at low strain. The results that emerge from molecular simulation are compared to an elastic theory of the buckling instability introduced by Read and co-workers. At high strain rates, significant differences are observed between elastic theory and simulation results for the buckling strain and the buckling wavelength. We explain this difference by the strain rate dependence of the mechanical response. A simple model that takes into account the influence of the strain rate in the mechanical response is presented to rationalize the results at low and moderate strain rates. At very high strain rates, cavitation takes place in the rubbery phase of the sample and limits the validity of the approach.