Purpose: Curved box-girder bridges offers an excellent solution to the problems associated with traffic congestion. However, owing to their complex geometry, they are subjected to shear lag, torsional warping and cross-sectional distortion, which must be assessed in their study and design. Furthermore, the dynamic behaviour of curved bridges adds to the complexity of the issue, emphasizing the importance of studying free vibration. The purpose of this study is to numerically model the concrete curved box-girder bridge considering torsional warping, distortion and distortional warping effects and to identify key parameters that influence the free vibration response of the box-girder bridge by validating it with experimental and analytical studies. Design/methodology/approach: The concrete bridge is numerically modelled by means of computationally effective thin-walled box-beam finite elements that consider torsional warping, distortion and distortional warping, which are prominent features of thinwalled box-girders. The free vibration analysis of the concrete curved box-girder bridge is performed by developing a finite element based MATLAB program. Findings: The identification of critical parameters that influence the free vibration behaviour of curved thin-walled concrete box-girder bridges is one of the main findings of the study. Each parameter and its effect has been extensively discussed. Research limitations/implications: The study limits for the preliminary design phase of thin-walled box-girder bridge decks, where a complete three-dimensional finite element analysis is unnecessary. The current approach can be extended to future research using a different method, such as finite element grilling technique on multi-span curved bridges having unequal span. Originality/value: The current research implements a finite element formulation in combination with thin-walled beam theory, where an extensive parametric study is conducted on the free vibration behaviour of a concrete thin-walled box-girder bridge, while also accounting for their complex structural actions. The validity of the given numerical formulation is demonstrated by a comparison of the natural frequencies found experimentally. The study carried out will be of great importance for engineers to help them anticipate the modal characteristics of a curved concrete thin-walled girder bridge, which will further be useful for evaluating their dynamic response analysis.