As a fundamental component of an automobile engine's timing chain drive system, the hydraulic automatic tensioner significantly enhances fuel economy while minimizing system vibrations and noise. However, there is a noticeable lack of research on automatic hydraulic tensioners. This study presents a comprehensive calculation approach for the principal parameters of a hydraulic automatic tensioner. An effective method, grounded in hydraulics and multibody dynamics, was introduced for estimating the dynamic response of such a tensioner. The simulation model developed for the hydraulic tensioner is characterized by its rapid dynamic response, consistent operation, and high accuracy. The dynamic behavior of the tensioner was analyzed under varying boundary conditions, using sinusoidal signal excitation. It was observed that the maximum damping force increases with a decreasing leakage gap. Conversely, an increase in oil temperature or air content leads to a decrease in the maximum damping force. The reaction forces derived from these calculations align well with experimental results. This calculation and simulation approach offers considerable value for the design of innovative hydraulic tensioners. It not only streamlines the design phase, minimizes the number of trials, and reduces product costs, but also provides robust insights for evaluating the performance of hydraulic tensioners.