Equations of motion for flexible multibody systems with model uncertainty are developed using the Lagrangian formulation. The dynamic model developed serves to exemplify systems which possess undesirable flexibility by representing it as a stochastic process. Further, a novel methodology for treating uncertainties in flexible systems is proposed. The method uses concepts from stochastic finite elements to address the problem of uncertain parameters in flexible mechanical systems. In particular, the problem of random bending rigidity of a flexible beam is studied. The spatial random process is represented using the Karhunen-Loeve expansion. The response process of the beam, comprising of large rotation and elastic vibration is expressed as a projection on the Homogeneous Chaos. Expressions for the response statistics, including the coupling between the elastic vibration and the large displacements are derived. Comparison of the results obtained with those from Monte-Carlo simulation shows a fair amount of agreement.