The mechanical properties of mullite $(3Al_2O_3;2SiO_2)$ environmental barrier coatings are determined using a laser-based ultrasonic system. The waveforms generated by a laser source in mullite coatings in the $1-20{mu}m$ thickness range are evaluated theoretically using the integral transform technique. It is shown that the laser source generated the two lowest order SAW modes in these systems. Experimental waveforms are generated using a 600ps pulsed Nd:YAG microchip laser and detected using a stabilized Michelson interferometer. The dispersion curves for the generated modes are extracted from the experimental data and the mechanical properties of the coatings are obtained by minimizing the error between the measured and calculated velocity values. The waveforms generated in mullite coatings agree well with theory and laser-based ultrasonics is shown to provide an effective tool for the nondestructive evaluation of ceramic coatings.