A computational design tool was developed to perform a constrained optimization of the acoustic environment within a vibrating cylinder, incorporating finite element and boundary element methods, The tool comprises a UNIX shell script that coordinates an iterative design optimization process integrating a number of programs, the key components of which are MSC/NASTRAN for structural analyses, COMET/Acoustics for acoustic analyses, and CONMIN for nonlinear optimization. In addition to the structure and implementation of the tool, this paper presents the results of a number of trials of the tool applied to stiffened and unstiffened cylinders, considering different formulations of the objective function to be optimized, and for a constant frequency exterior monopole excitation. Models were constructed to investigate longitudinal vs circumferential variations in design properties as well. The results indicate that shell thickness variations tend to dominate interior acoustic response, as compared with stiffener variations. The results further indicate that longitudinal variation is more effective than circumferential variation. Effective longitudinal design variations include shell thickening toward the cylinder midplane or, equally effective, thinning toward the midplane, Effective circumferential designs exhibited periodic variation around the circumference.