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Consideration is given to results of experimental and theoretical investigations how alpha-epsilon phase transition in the unalloyed iron and the 30 KhGSA steel and its absence in the austenitic 12Kh18N10T stainless steel influence processes under explosive deformation of spheres made of these materials. Polymorphous transition is shown to significantly effect on: amount of explosion-products energy transferred to a sphere, evolution of the converging-wave structure and its parameters, profiles of stress wave and temperature T (R, t) for some Lagrangian particles along the sphere radius, character of energy cumulation under spherical convergence of waves. Int. J. Model. Simul. Sci. Comput. 2015.06. Downloaded from www.worldscientific.com by NANYANG TECHNOLOGICAL UNIVERSITY on 08/24/15. For personal use only. 1550001-2 Int. J. Model. Simul. Sci. Comput. 2015.06. Downloaded from www.worldscientific.com by NANYANG TECHNOLOGICAL UNIVERSITY on 08/24/15. For personal use only.