Abstract: Two non-perfect converging conical shock wave models, one with angle of attack and the other with ovality, were proposed to investigate the different behaviors of conical shock wave convergence with a deviation from the perfect axisymmetric condition. The investigation was carried out by using experimental observation in shock tunnel and numerical simulation. The results show that the circumferential non-uniformity in shock intensity caused by the angle of attack is enlarged due to the flow convergence, which results in remarkable differences between the windward and the leeward sides. The greater the angle of attack is, the stronger the non-uniformity of the shock intensity is, and the more likely the shock front becomes discontinuous with formation of kinks during the converging process. The convergence of the shock is weakened after the appearance of the kinks. On the other hand, the initial geometric non-uniformity of the shock caused by the constraint of ellipse exhibits a different behavior of shock intensification particularly between the direction of the major axis and the minor axis. The intensity of the shock increases faster along the major axis direction. The larger the aspect ratio of the ellipse is, the stronger the geometric non-uniformity of the initial shock is. During the converging process, the difference of shock intensity between the major and minor axes becomes more prominent, and more likely the shock front grows to form discontinuous kinks. The present research on the two models demonstrates that the inevitable occurrence of Mach reflection at the center will disappear and regular reflection shows up instead with a sufficient deviation from the perfect axisymmetric condition.