This study proposes an analytic method that determines an optimal arrangement of absorptive materials on an enclosure surface. Under the optimal arrangement, a quiet zone in the enclosure has the minimum εp/ (acoustic potential energy density). The proposed method has been implemented by using a BEM simulation and a genetic algorithm. The BEM simulation evaluates the εp/ under the prescribed arrangement of the absorptive materials. The genetic algorithm searches the optimal arrangement by referring the ep evaluated from the BEM simulation. In the BEM simulation, the absorptive material arrangement is expressed as a vector, which is denoted as in absorptive material arrangement (AMA) vector. Besides, an admittance vector of which elements are admittances of available absorptive materials and an AMA matrix that transforms the admittance vector into the AMA vector are defined. The AMA matrix is also used as a chromosome in the genetic algorithm so that it functions to relate the BEM simulation to the genetic algorithm. As a verification example, the proposed method is applied to make the quiet zone in a parallelepiped enclosure.