In this paper, we present a dynamic model for a generic drill-string. The model is developed with the intention for component-based simulation with coupling to external subsystems. The performance of the drill-string is vital in terms of efficient wellbore excavation for increased hydrocarbon extraction. Drill-string vibrations limit the performance of rotary drilling; the phenomenon is well-known and still a subject of interest in academia and in industry. In this work, we have developed a nonlinear flexible drill-string model based on Lagrangian dynamics, to simulate the performance during vibrations. The model incorporates dynamics governed by lateral bending, longitudinal motion and torsional deformation. The elastic property of the string is modeled with mode shape functions representing the elastic deformation, with a finite set of modal coordinates. By developing a bond graph model from the equations of motion, we can ensure correct causality of the model towards interacting subsystems. The model is analyzed through extensive simulations in case studies, comparing the qualitative behavior of the model with state-of-the art models. The flexible drill-string model presented in this paper will aid in developing simulation case studies and parameter identification for offshore drilling operations.