Purpose <p>As an integral part of the drill string, drilling jars effectively address pipe-stuck issues by delivering substantial impact forces when the bottom-hole assembly becomes stuck. However, due to the complex dynamic interactions between the drill string and the borehole wall, as well as the significant geometric nonlinearity of the drill string, existing analytical and numerical methods—which often rely on simplified assumptions, such as linear elastic behavior or neglect of contact interactions—struggle to accurately characterize the impact forces and performance of drilling jars.</p> Methods <p>This study incorporated stochastic contact theory to develop a three-dimensional transient dynamic model for both up and down jarring operations under realistic wellbore trajectories, by using an explicit integration algorithm. The fluctuations of axial force at the jar and stuck point were captured to analyze the coupled dynamic nonlinear effects and to evaluate jar performance. Additionally, the influence of factors such as jar type, jar load, and stroke length on performance was investigated.</p> Results <p>During jarring operation, the elastic strain energy stored in the drill string is rapidly transformed into piston kinetic energy once the hydraulic chamber is released, causing the axial force near the jar to drop abruptly to zero. Subsequent piston collision generates significant axial excitation loads that propagate along the drill string, inducing pronounced force fluctuations and vibration responses, and ultimately producing a release force at the stuck point.</p> Conclusion <p>The jar load is the dominant factor governing impact efficiency, as it substantially enhances both impact and release forces while reducing impact delay time. By contrast, stroke length primarily affects the timing of impact, showing negligible influence on force magnitude during up-jarring but increasing both forces during down-jarring due to the gravitational effect of the drill string.</p>