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The main contribution of this work is validating the Ludwick law to model the nonlinear mechanical behavior in the prediction of the critical buckling load of nonlinear elastic columns. The critical buckling loads of specimens with different slenderness ratios were obtained by conducting experimental tests on flax/PLA columns with pinned–pinned boundary conditions. The modified Ludwick law parameters were calibrated to fit the stress–strain curve obtained in tensile tests of flax/PLA specimens. The flax/PLA specimens were manufactured using the compression molding method. Moreover, a numerical model considering the Marlow hyperelastic constitutive model was used to predict the critical buckling load. Theoretical predictions using Ludwick law and numerical results were in excellent agreement with experimental data. Results showed that the maximum error of the numerical predictions for critical buckling load is 14.3%, and the maximum error of the theoretical predictions is 8.0%. Additionally, a parametric study was developed to analyze the influence of material's nonlinearity on the numerical prediction accuracy of the Marlow model.