Using Fourier transform rheology the Giesekus, exponential Phan-Tien and Tanner, and modified eXtended Pom-Pom constitutive models were examined in the non-linear regime represented by large amplitude oscillatory shear (LAOS) measurements. For the experiments a 5 wt% solution of poly(ethylene oxide) (molecular weight 1000 kg/mol) solved in dimethyl sulfoxide was used. The minimal number of harmonics required for an adequate reconstruction of the original raw time-stress signal was shown. An emphasis was paid to simultaneous consideration of the normalised stress magnitudes and the phases of individual harmonics in the fitting procedure adjusting the non-linear parameters of the studied constitutive models.