We will explain a new method for obtaining the nearly optimal domain for optimal shape design problems associated with the solution of a nonlinear wave equation. Taking into account the boundary and terminal conditions of the system, a new approach is applied to determine the optimal domain and its related optimal control function with respect to the integral performance criteria, by use of positive Radon measures. The approach, say shape-measure, consists of two steps; first for a fixed domain, the optimal control will be identified by the use of measures. This function and the optimal value of the objective function depend on the geometrical variables of the domain. In the second step, based on the results of the previous one and by applying some convenient optimization techniques, the optimal domain and its related optimal control function will be identified at the same time. The existence of the optimal solution is considered and a numerical example is also given