One of the main issues on seismic design of bridges is the determination of strong ground motion application direction in order to capture the most unfavorable situation. The most common approach to this problem is known as 30% combination rule. In this approach, one of the two horizontal components of the strong ground motion record is applied in one principal direction of the bridge whereas the remaining horizontal component is applied to the other direction. Then, the resultant response is calculated by simply adding the results of the first case to the 30% of the results of the second case. In order to get the envelope, the reverse condition is also investigated. However, 30% combination rule is applicable only for the structural elements having an elastic behavior under seismic loads. Thus, for bridge elements such as columns and cap beams which can go beyond the elastic range, 30% combination rule may not provide reliable results. On the other hand, choice of the horizontal component of strong ground motion to be applied in which principal direction of the bridge is another problem to deal with while performing nonlinear response history analysis. Furthermore, in nonlinear response history analysis, deciding the angle of attack of ground motion in which the most unfavorable situation can be captured is a distinctive property depending on the rigidity and skewness of bridges. In this study, two types of bridges are investigated one of which is characterized to be rigid and the other is flexible. Both types of bridges are modelled for 7 different skew angles starting from 0 degrees up to 60 degrees in an increment of 10 degrees. Therefore, 14 models are created for variable geometrical properties. A series of nonlinear response history analysis are performed for each of them at 12 particular angles of attack starting from 0 degrees with an increment of 15 degrees at each step up to an angle of 120 degrees. Moreover, these analyses are repeated for 7 different strong ground motion records and sensitivity analyses are accomplished. Change in column moments and curvatures in strong and weak axis are examined as seismic demand parameters. At the end of the study, strong dependence of critical angle of attack on the skewness and rigidity properties of the bridges is emphasized.