The non-symmetric responses of normal stresses in oscillatory squeeze flow have been investigated with model calculations. The simplest and most widely used constitutive equations were employed to predict the non-symmetric normal stresses, which is a distinctive feature of oscillatory squeeze flow. The model prediction was compared with experimental data of polymer solution in terms of stress shape, Lissajous plot, stress decomposition, and Fourier transformation. The upper-convected Maxwell, Giesekus, and exponential Phan-Thien Tanner models predicted the nonsymmetric characteristics of normal stresses under oscillatory squeeze flow. The predictions showed fairly good agreement with experimental data. However, the upper-convected Maxwell model showed unrealistic result in the Lissajous plot of [stress vs. strain] and [stress vs. strain rate]. From stress decomposition, it could be confirmed that the non-symmetric nature arises from the elastic contribution of the normal stress, which was verified in both experiment and model calculation. This study is expected to provide useful insights for further understanding of the nonlinear and non-symmetric characteristics of oscillatory squeeze flow.