The Rayleigh beam equation is the formal limit of the Timoshenko beam equation as the shear modulus K --> +infinity. Following a method in W. Littman, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 5 (1978), pp. 567-580 and W. Littman, Proc. 24th IEEE CDC, Fort Lauderdale, FL, 1985, controllability is possible. That is, the evolution systems associated with the Rayleigh and Timoshenko equations can be driven to rest by applying appropriate controls at both ends of the beam. In this work we show that the process is uniform; more precisely, controllability of the Rayleigh system can be achieved by letting K --> +infinity in the solution of the Timoshenko controllability problem.