Passing maneuvers on rural two-lane highways require drivers to enter the opposing traffic lane to overtake an impeding vehicle. A successful maneuver requires the driver to correctly judge the time it will take to complete the pass, and the distance to and speed of the oncoming vehicle. Previous studies have shown that the type and speed of impeding vehicle, traffic volume, roadway cross-section, and driver characteristics influence gap-acceptance behavior, but have not considered vertical curvature or specified directionality in the horizontal curvature. This paper describes a driving simulation experiment in which these geometric, situational, and driver characteristic variables were collected for 643 passing attempts. A logistic regression model was developed to infer the effects of horizontal and vertical curvature on driver passing decisions. This study uniquely quantified that drivers were: more likely to pass if the road curved to the left than if it was straight and less likely to pass if the road curved to the right; more likely to pass if there was a sag curve than if the road was flat and less likely to pass if there was a crest curve; and less likely to pass when traveling uphill than if the road was level. As the influence of roadway geometry on gap-acceptance decisions is not currently implemented in overtaking models, the results of this study have practical implications for microsimulation of rural two-lane highways, highway design, and highway safety, and the inclusion of roadway geometry variables may improve future modeling of roadway capacity and passing locations along two-lane highways.