This paper proposes a method by analysing the free vibration behavior of various polymers for fatigue strength property characterisation. Four disc-shaped specimens with different types of polymer were prepared, namely polyethylene, polycarbonate, polyoxymethylene and polyamide. Experimental dynamic tests were carried out based on ASTM E1876 to measure the transient vibration characteristics using an accelerometer positioned on the flat of the disc close to the outer circumference. The specimen has been lightly striked for pulse loading at the center point using an impact hammer. Using the method of Mesokurtosis Zonal Nonparametric (M-Z-N), the instantaneous data point of the selected decaying signals have been analysed and from the obtained results, the correlation between the M-Z-N coefficient and fatigue strength property has been investigated. It is revealed that the proposed statistical signal analysis method can be applied on the transient impulsive free vibration signal for effectively characterise fatigue strength property of polymers.