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In micromechanics, the definition of the optimum Representative Volume Element (RVE) that represents the microstructure of the considered composite material is still an ongoing research subject. Therefore, depending on the required accuracy of the micromechanical model predictions, the size and number of realizations that define the RVE, must be determined through a systematic study. In the present work, an RVE based study is conducted on precipitation hardened NiTi Shape Memory Alloys (SMAs) with Ni₄Ti₃ precipitates. The considered RVEs consist of a homogeneous SMA matrix with periodically arranged precipitates. The precipitates are assumed to have ellipsoid shape and are arranged in random position and orientations, ensuring the periodicity at the boundaries. The non-linear constitutive behavior of the precipitated SMA, is solved by means of a recently developed Fast Fourier Transform …