This study aims to investigate the behavior of skewed and straight highway overpass bridges both with and without taking into account the effects of Soil-Structure Interaction (SSI) due to near-fault ground motions. Both deterministic (i.e., pushover and nonlinear dynamic analyses) and probabilistic approaches were utilized. A set of response sensitivity analyses was performed considering various skew angles, column elements, and soil properties for bridge considered both as fixed-base and SSI models. It has been observed that as the skew angle increased, the bridge responded more severely to the ground motion. For instance, the deck rotation and shear-keys displacement increased with an increase in the skew angle. A modal pushover analysis was also performed in conjunction with the nonlinear dynamic analysis. It has been found that combining the bridge responses for various modes of vibration resulted in a relatively accurate seismic response compared to the nonlinear dynamic analysis while saving time and analysis cost, to a great extent. A probabilistic analysis was also performed considering record-to-record variability in ground motion, and a set of probabilistic seismic demand and fragility plots was generated. The effects of change in the skew angle and also SSI were studied to see various bridge responses. The damage probability increased especially with respect to deck rotation as the skew angle increased. The SSI had a decreasing effect on the overall response of the bridge with pile foundation.