In vibration fatigue, flexible structures operate at or close to their natural frequencies. Therefore, it is common to consider the input excitation as well as the stress/strain response of the structure to be Gaussian and stationary. In reality, a non-Gaussian and non-stationary excitation is frequently observed, resulting in a possibly non-Gaussian and non-stationary response. The importance of this non-Gaussianity (typically observed via the kurtosis) has resulted in significant research on the relevance of the Gaussian assumption in fatigue life. For dynamic structures the prior research was mainly theoretically and numerically focused. This work researches the importance of non-Gaussianity and non-stationarity theoretically, numerically and experimentally. Y-shaped specimens were used in this research. The excitation close to the natural frequency is random and in all the researched cases with the same power spectral density (PSD). While the PSD was kept the same, the rate of non-Gaussianity and the non-stationarity were changed. The results show that when the excitation is stationary and non-Gaussian, the fatigue life is not significantly impacted, and that standard frequency-counting methods are applicable. However, for the case of a non-stationary, non-Gaussian excitation, the fatigue life was found to be significantly impacted and the Gaussian theoretical approach is questionable.