Ductile materials break into multiple fragments under rapid tension loadings. The Mott-Grady analysis, which is based on the unloading wave (the Mott wave) propagation theory and a linear cohesive fracture law, gives the lower limit estimation of the average fragment size for ductile materials. As the damage evolution process is complicated, the ductile fragmentation process may be affected by the types of the cohesive fracture law. In this research, we present a theoretical analysis of the Mott wave propagations under different boundary conditions, which provides estimations of the fragment size for linear or nonlinear cohesive fracture model. Numerical simulation using ABAQUS/Explicit code reproduced the tensile fragmentation process of ductile steel bar under high strain rates. Both the theoretical analysis and the numerical simulations show that the fracture law to be used has a significant influence on the fragmentation process of ductile metals, therefore causing the fragment number to vary. Detailed results of the analysis will be given in the presentation.