Abstract: We study the theory of free wobble of the triaxial Earth and find that the Euler period should be actually expressed by the complete elliptic integral of first kind and the trace of the free polar motion is elliptic and the orientations of its semi-minor and major axes are approximately parallel to the Earth's principal axes A and B, respectively. Due to the triaxiality of the Earth, there is a mechanism of the frequency-amplitude modulation in the Chandler wobble which might be a candidate to explain the correlation between the amplitude and the period of the Chandler wobble. We compared the theoretical polar parameters (m1,m2) with the observed values for the Chandler components obtained from the data EOP (IERS), and find that they coincide with each other quite well, especially in recent years. Moreover, a polar wander towards 77.98°W at the rate 3.93 mas/a was also obtained from the IERS data.