Abstract: High friction and torque remain common challenges in extended-reach drilling. Current research primarily focuses on the development and solution of wellbore trajectory design models, with limited investigation into the specific effects of trajectory characteristic parameters on friction and torque. In this paper, based on the lateral catenary mathematical model, a wellbore trajectory design model and a coupled analysis model for friction and torque are established. A case study is conducted to compare the design performance of the lateral catenary trajectory with the traditional three-section circular arc trajectory. Furthermore, the influence of key parameters—including kick-off point depth, transition section characteristics, and maximum inclination angle—on the friction and torque of the lateral catenary trajectory is analyzed. Results indicate that, compared to the circular arc trajectory, the lateral catenary trajectory achieves lower friction during tripping out, tripping in, and slide drilling, as well as reduced torque during rotary drilling. Increasing the kick-off point depth generally leads to higher friction. Variations in transition section parameters result in complex changes in friction and torque with build-up rate and inclination angle. Increasing the maximum inclination angle initially causes a significant decrease in friction and torque, followed by a diminishing rate of reduction. The findings demonstrate that the lateral catenary trajectory offers distinct advantages in reducing friction and torque. Selecting an appropriate combination of trajectory parameters during design can effectively mitigate drilling friction and torque. The research provide a valuable reference for field wellbore trajectory design.