Abstract The theories of elastic and inelastic stabilities are used to describe the behaviour of the wheat plant under axial and lateral applied forces. A theoretical analysis of the structure of the plant and its stability is presented along with experimental data on the plant's elastic and visco-elastic parameters. The influence of the cross-sectional variation, wind forces and the irregular shape of the plant structure on the critical load and deformation shape are presented theoretically. Experimental data on critical loads, deformation curves and the type of buckling, i.e. elastic, elastic-plastic or plastic are included. The effect of maturity on the plant's elastic and visco-elastic parameters is discussed.