Abstract : Fiber reinforced layers are very popular in industry but are prone to structural instabilities observed in various experimental and technological environments. Such situations combine global inplane buckling of reinforcing fibers and local shearing or compression of filling material. The purpose of the work is to develop enriched multiscale models, able to treat both aspects through an adequate kinematic description of the different components and a proper exchange of information between local and global models. The macroscopic level introduces in addition to the filling material a surface density of beams able to resist against in plane and out of plane bending. A new finite element model is then developed at this macroscopic level and we show through theoretical analysis and numerical tests that the model is locking-free. At microscopic level, a local cell model is introduced and justified through asymptotic analysis, model which is then solved by a local nonlinear finite element model. Some numerical precautions are added in the multiscale approach to avoid a numerical locking on incompressible materials. In addition, a multiscale stability analysis is conducted in buckling situations predicting the critical load and the corresponding buckling mode. The models are finally validated on available experimental set up.