This paper describes the general theory and method of calculating drag force while tripping in directional wells. The application of the theory has demonstrated that the drag force created in the quadratic parabola trajectory while tripping is smaller than that of the catenary path no matter whether the dead weight of drill string is considered or not. Based on the analysis of the approximation of catenary equation, the changeability and uncontroliability of the downhole horizontal tension, and randomness of the design, it is believed that the theoretical trajectory of catenary path does not coincide with the actual drill string catenary trajectory in a well, and thus the expected results can not be obtained. The degree of difficulty in drilling, completion, production and some other downhole operations is compared between the two trajectories. It is concluded that the directional wells with quadratic parabola trajectory offer more advantages than those with catenary path.