Based on a robust numerical method for calculation of band structure for stress-waves in heterogeneous media, a layered composite was designed and fabricated. It is shown that in the second pass band of this simple 2-phase layered structure, the direction of the energy flow is opposite that of the phase velocity. The ultrasonic stress-wave transmission through multiple thicknesses of this structure was studied experimentally and various quantities, such as band structure, phase velocity, group velocity, and a representation of the velocity of energy propagation were measured and compared with numerical predictions. The numerical calculations are based on hybrid (mixed min-max) variational principles presented previously by Nemat-Nasser and coworkers. In the cases where a closed form solution exists, the numerical results of this method agree very accurately with the results of the exact solution. Furthermore, the computational efficiency of the mixed variational method renders it an excellent tool for design and analysis of stress-wave propagation in heterogeneous media.