In elliptical vibration cutting (EVC), cutting performance is largely affected by the shape of an elliptical path of the cutting tool. In this study, two parallel piezoelectric actuators were used to make an elliptical vibration cutting device. When harmonic voltages of $90^{circ}$ out-of-phase are supplied to the EVC device, creation of an ideal elliptical trajectory whose major and minor axes are parallel to the cutting and thrust directions is anticipated from a kinematic analysis of the EVC device, however, the paths we experimentally observed showed significant distortions in its shape ranging from skew to excessive elongation of the major axis of the ellipse. To compensate distortions, an analytical model describing the elliptical path of the cutting tool was developed and verified with experimental results, and based on the analytical model, the distorted elliptical paths created at 100 Hz, 1 kHz, and 16 kHz were corrected for skew and elongation.