The time it takes to clear road traffic incidents is an important performance measure in highway management. Understanding the effects of explanatory variables on incident clearance time is a necessary step in developing incident management strategies. Previously, hazard-based duration models have been used extensively in identifying the influential factors in incident duration. Quantile regression models have been introduced in survival analysis, and these offer a more flexible approach to analyse incident duration data. The advantage offered by quantile regression lies in the ability to make inferences about the effect of explanatory variables on different quantiles of the incident duration distribution. In this work, quantile regression was applied to an incident clearance time dataset collected on freeway sections in Seattle, USA. Based on the estimation results from quantile regression, four influential factors were identified to have a stronger impact at the upper tail of the clearance time distribution. These factors cannot be identified through the conventional hazard-based duration methods used in most previous studies. The findings of this study suggest that the additional information obtained from quantile regression about the short-term and long-term effects of explanatory variables is potentially useful for assigning clearance priority to different road traffic incident types.