In this paper, an analytical method that can describe the structural behaviour of prestressed concrete (PSC) bridges with unbonded external tendons is developed. Since the unbonded external tendon is directly connected to the deviators while maintaining a straight configuration, it has a different deformation field from that of concrete and accompanies a secondary effect caused by the change of the primary eccentricity between the concrete and external tendon. The friction slip at the deviators is also taken into consideration on the basis of the force equilibrium between the friction force and the driving force. Moreover, all the material non-linearities and time-dependent deformations such as creep and shrinkage of concrete and relaxation of the tendon are included because the centroidal axis of a section changes according to cracking and time-dependent effects in the constituent materials. Through correlation studies between experimental data and analytical results, it is verified that the proposed numerical model can effectively predict the structural behaviour of PSC bridges with comparative precision.