Horizontally curved concrete girder bridges have complex dynamic characteristics because of their asymmetry and non-uniform mass and stiffness distribution. Their seismic behaviour is considerably affected by various such as structural characteristics, radius of the superstructure curvature and local site conditions. The computational, three-dimensional (3D) bridge models consisting of concrete girders with concrete deck, single pier columns and caps were created in OpenSees analyzing a representative, three-, four- and five-span continuous curved concrete girder bridges in N. Macedonia. Different seismic hazard levels and soil conditions were chosen in order to perform site-specific hazard calculations to investigate the effect of critical curved bridge parameters on the seismic response using a group of representative bridges. Two levels of capacity were considered: damage and collapse limit state (DLS and CLS). The results from the performed extensive nonlinear analyses including uncertainties were used to estimate the influence of the number of spans, deck width, pier height, deck horizontal curvature radius and local site effects on the bridge performance. The influence of soil conditions and superstructure curvature are significant for the seismic vulnerability of girder bridges, especially those with more spans. With the increase of the superstructure curvature radius, the bridges become more vulnerable, particularly if they have more spans and are founded on soil of weaker characteristics. The difference in the probability of damage occurrence to bridges with smaller number of spans, regardless the curvature radius, is small if these are founded on a good base. In the case of CLS, such probability differs extensively, particularly in multi-span bridges founded on weak soil. Regardless the curvature radius and the soil characteristics, the width of the superstructure has a favorable effect upon the seismic response of the selected type of bridges. Bridges with piers of a greater height and greater curvature radius exhibit considerably less favorable seismic behavior than bridges of smaller curvature radius founded on better soil.