We consider in this paper the existence and numerical estimation of the distributed control of a nonlinear wave equation with an integral performance criterion and fixed final states. The problem is modified into one consisting of the minimization of a linear form over a set of pairs of positive measures satisfying linear constrains. The minimization in the new problem is global and can be approximated by a finite-dimensional linear programming problem. The solution of this problem is used to construct a nearly optimal control. An example is given to illustrate the procedure.