Abstract Thermoacoustic engines are devices suitable to convert heat into acoustic energy and viceversa. They are basically composed with a porous medium and two heat exchangers inserted into a resonator or looped tube. Depending on the phase shift between the sound pressure and the particle velocity of the working fluid, two categories of engines can be realized: standing-wave or travelling-wave devices. Thermodynamic performance of thermoacoustic engines strongly depends on the structural properties of the porous material and the geometric features of the device. In a previous work the authors developed a procedure for optimizing the properties described above to obtain, for a standing-wave device, the maximum acoustic power, given fixed boundary conditions. In this work, the above-mentioned procedure has been extended also for a traveling-wave engine.