Open-ended pipe piles (OEPPs) are widely used in offshore foundations, yet accurately predicting their driving responses remains challenging due to soil plug complexities. Existing pile driving analysis models inadequately characterize the effects of soil plug, potentially leading to driving problems such as hammer refusal, pile running, and structural damage. This paper proposes an effective soil plug (ESP) model for OEPP driving analysis. The ESP model considers the effective range of soil plug, which exerts internal resistance that increases exponentially with depth while the beyond of effective range contributes only mass inertia. It also accounts for the relative slippage at the pile-soil plug interface. A differential iterative method is developed to solve the ESP model. Subsequently, investigations including the model validation and parameter analysis are conducted. Model validations against existing models and field measurements confirms the reliability of the ESP model. Parameters sensitivity analysis reveals the importance of soil plug length and distribution type of internal resistance on the pile dynamic responses. In addition, if soil plug slippage occurs, the displacement peak of soil plug increases with depth rather than one-dimensional wave attenuation. Furthermore, contrary to previous assumptions of continuous slippage, the soil plug experiences a discontinuous jump-sliding mode under long-duration impact loading. These findings provide theoretical basis for OEPP driving simulation and interpretations of high-strain dynamic test.