The present work aims to analyze the buckling behavior of nonlinear elastic columns with different open cross-sections and slenderness ratios to verify the limits of the modified Ludwick law to predict the critical buckling load. The results of the analytical formulation based on the modified Ludwick law are compared with a FEM numerical model using the Marlow hyperelastic behavior and experimental results conducted on flax/PLA specimens with three different open cross-sections. The comparative results show that the numerical predictions agree with the experimental results in all the cases. The FEM model can exactly reproduce the buckling behavior of the C-section columns. However, the prediction errors for the C90 and C180 columns are higher than for the C60 columns. Moreover, the theoretical estimations indicate that the C90 cross-section column is the limit of application of the modified Ludwick law to predict the critical buckling load of nonlinear elastic columns with open cross-sections, and the C180 column is out of the prediction limits. Generally, the numerical and theoretical models underestimated the scattering effects of the predictions because more experimental variables were not considered by the models.