Shape memory alloy (SMA) bidimensional cellular structures (CSs) have a great potential application in attenuation of vibrations due to reversible martensitic phase transformations induced by thermal or mechanical loading. This work aims to produce a thermal and mechanical characterization of CuAlMn SMA CSs produced by rapid investment casting (RIC). Structures with different unit cell geometries and thicknesses of 0.5 mm and 1 mm were manufactured by centrifugal RIC. Compression tests at different temperatures were performed on the CS to verify its thermomechanical behavior. We observed that a CS with a thickness of 0.5 mm presents greater mechanical strength and lower levels of maximum force at the end of each 5% compression cycle, ranging from approximately 1/10 to 1/3, compared to structures with a thickness of 1 mm. Among all the CS configurations, the re-entrant structure exhibited higher levels of force, with higher secant stiffness and dissipated energy. The structures resisted the application of compressive forces that varied between 125 N and 500 N for the 0.5 mm CS and between 500 N and 5500 N for the 1 mm CS. Therefore, the results showed that all CuAlMn SMA CSs produced by RIC exhibited sufficient strength to attain strain levels of up to 5% at different temperatures, and that the unit cell geometry can be used to tune the mechanical properties.