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The mechanical resonant response of a solid depends on its shape, density, and elastic moduli. We describe here the instrumentation and computational methods for obtaining and analyzing the resonant frequency of very small (0.001 cm3) samples, and provide examples to demonstrate the utilization of the technique. A new material type with six independent elastic constants are formulated and tested with the instrumentation. This study will leads to expansion of the software capability for the testing of novel materials.