The controllability of the wave equation with a viscous damping on a bounded interval is considered. The exterior force is taken in the formwithas a control. Necessary and sufficient conditions for exact controllability are established. Such a control brings the oscillating string to rest in a finite time, T. These results are a generalization of the well-known results by D. Russell for an undamped string. The techniques are based on the theory of nonselfadjoint operators in a Hilbert space. Two facts are crucial for this approach. Namely, the set of eigenfunctions of the dynamic generator of the evolution system forms a Riesz basis in the energy space; and the family of nonharmonic exponentials generated by the eigenvalues of the problem forms a Riesz basis in the space. The value of T coincides with the value found by Russell for a continuum without damping.