The presence and distribution of Ni₄Ti₃ particles in NiTi alloys have a significant influence on martensitic phase transformation path by favoring the formation of R–phase rather than B19’ phase since the latter produces larger lattice deformation. To deeply understand the above, some experimental studies have been done by using differential scanning calorimetry (DSC) and in situ transmission electron microscopy (TEM). Meanwhile, some preliminary simulations have also been performed focusing on the morphology evolution of single and multiple Ni₄Ti₃ variants in single NiTi alloy system as well as considering the effect of external loads on selective precipitate growth. Whereas, in engineering application, the NiTi alloys often undergo the external load which may affect the growth kinetics of Ni₄Ti₃ precipitates. Therefore, it is necessary to investigate the effect of applied load on growth kinetics of Ni₄Ti₃ precipitates. In this paper, the phase field method has been extended to study the microstructure evolution and growth kinetics of Ni₄Ti₃ precipitates in NiTi alloys during zero–stress and stress–assisted aging. The simulation results show that during stress–free aging, four groups of the variants precipitate along the corresponding (111)_B2 habit plane; when the NiTi matrix is under <111>_B2 comprssive stress–assisted aging, there is only one group of the variants with the normal lines parallel to <111>_B2 to be precipitated. Although the uniaxial compressive stress apparently promotes the nucleation and slightly accelerates the growth of Ni₄Ti₃ variants in each group, the trends of aging time dependences of the area fraction, variant length, variant width and length–width ratio seem unchanged. The larger stresses can cause length and width of the variant slightly larger, but the area fraction of the Ni₄Ti₃ particles increases with increasing stress level. The simulation results are in good coincidence with the experimental results available.