We consider a system described by the Euler-Bernoulli beam equation, with one end clamped and with torque input at the other end. The output function are the displacement and the angle velocity at the non-clamped end of the beam. We study the identification of the spatially variable coefficients in the beam equation, from input-output data. We show that both the density and the flexural rigidity of the beam (which are assumed to be of class C-4) can be uniquely determined if the input and output functions are known for all positive times. (C) 2007 Elsevier Ltd. All rights reserved.