Buckling is a significant nonlinear deformation that can occur to beams under high compression loading. Pentamodes are lattice structures composed by beams and are designed to have high bulk modulus. Thus, they can confront high compression loading conditions [1-2], and buckling phenomena may occur. In addition, due to the non-homogeneous nature of pentamodes, the response of pentamodes under loading conditions is also affected [3]. Their wide applications field, from aerospace structure to vibrations isolation structure (antiseismic design) contribute to further investigation of buckling characteristic of pentamode structures. In our study, a numerical investigation of pentamodes under compression loading conditions has taken place. Pentamodes with and without confinement plates and with different height are considered. The present numerical study deals with the buckling response of pentamodes structures. More specifically, the main objective is the investigation of failure mechanism of pentamodes structures under high compression force, which contribute to buckling, using the Finite Element Method (FEM). The aforementioned procedure is implemented using FEM packages which incorporates nonlinear FEM analyses and buckling analysis. The elastoplastic material behaviour of Clear V4 polymer [4] is modelled using a bilinear stress-strain relationship. In addition, large displacement analyses have taken place. The convergence of the algorithm was tested under different pentamode structures, with and without confinement plates. Load displacement curves have been created using the results from the FEM analyses. In addition, Von Mises stress contours have been developed to locate maximum stress fields and their amplitude taking into consideration material and geometric non linearity. It was also found that pentamodes appear to rotate under compression loading, due to their non-homogenous nature. REFERENCES [1] F. Fabbrocino, A. Amendola, F. Benzoni and F. Fraternali, Seismic Appilcation of Pentamode Lattices, International Journal of Earthquake Engineering, 62-71, 2015. [2] Amendola A , Carpentieri G , Feo L , Fraternali F . Bending dominated response of layered mechanical metamaterials alternating pentamode lattices and confinement plates, Composite structures. 157, 71–77, 2016 [3] Lin G., Li J., Chen P., Sun W., Chizhik S. A., Makhaniok A. A., Melnikova G. B., Kuznetsova T. A., Buckling of lattice columns made from three-dimensional chiral mechanical met