A series of experiments of strain modulations in heterostructures of SrTiO3/LaAlO3 and LaAlO3/SrTiO3 perovskite thin films fabricated by laser molecular beam epitaxy (L-MBE) were performed to study the effect of the compressive stress and tensile stress on the growth and microstructure of the films. The growth process of the films was in-situ monitored by reflective high-energy electron diffraction (RHEED). The morphology of the films was studied by ex-situ atomic force microscopy (AFM). We demonstrated that the compressive stress-induced self-organized SrTiO3 films deposited on LaAlO3 (100) single crystal substrates exhibited a periodic well-ordered ripple-shaped structure, forming a unique nanopatterning tool to fabricate 1D/2D arrays of confined nanostructures (i.e., islands and wires). Small angle X-ray scattering technique was employed to investigate the superstructure. Symmetric satellite peaks were observed, which also revealed the well-aligned self-organized structures. In contrast, the similar superstructure was not observed during the growth of the tensile stress-induced LaAlO3 films on SrTiO3 substrates. Based on the experimental data, the compressive stress was estimated as the main reason of the self-organized growth. A growth model about the formation mechanisms of compressive stress-induced nanostructure was put forward and systematical kinetics elucidations about the growth processes were also discussed to illustrate the effects of different stresses on the growth and microstructures of the films.