The influence of parameters such as temperature, density of the critical current j c , sample dimensions and heat exchange conditions on the critical state stability has been studied in thin samples of textured Bi 2 Sr 2 CaCu 2 O 8+d (BSCCO) superconductor, in an external magnetic field perpendicular to the wide surface of the samples. The results show that stability of the superconductor against flux jumps increases with decreasing sample thickness. A composite-like sample consisting of two superconducting slabs glued together exhibits critical state stability as a bulk sample of the same thickness while it is less stable against flux jumping than the unit slab. The field of the first flux jump H fj1 decreases with increasing magnetic field sweep rate. For a given temperature there exists a critical sweep rate below which flux jumps vanish. These observations are interpreted in terms of the current distribution in thin superconducting samples characterized by a strong demagnetizing factor. The results are compared with a model developed for samples characterized by negligible demagnetizing effects. The critical state stability in BSCCO has been discussed in terms of the diffusion of heat and of the magnetic flux within the superconductor and the influence of heat exchange on these conditions.