| We investigate the mechanisms of nonsequential double ionization (NSDI) of atoms as exposed to ultra-strong and ultra-fast laser fields through numerical and analytical simulations. As the well-known strong field approximations have explained many phenomena about NSDI, the Coulomb and multiphoton effects are not included, which have been shown to be important in the process of NSDI. And the numerical study of the NSDI based on the time-dependent Schrodinger equation, is limited by the high-dimension simulations involved in the theoretical description of two-electron dynamics. So in this paper, we use one-dimensional two-electron model with every electron having one degree of freedom to study the NSDI. Because of the complexity of the total momentum distribution of correlated NSDI electron pairs, we use the “snapshot” method to observe the momentum distribution. Namely, at one moment, a proper range of wave function is selected and Fourier transform of the selected wave function produces the momentum distribution of correlated electron pairs. We find that the range of the selected wave function has significant influences on the shape of the two-electron momentum distribution, and hence on analyzing and studying the NSDI. On the basis of classical three-step model, we analyze the dynamics of correlated electron pairs in NSDI and find the applicable range of the selected wave function to observe two-electron momentum distribution. We analyze the dynamics of different NSDI mechanisms in detail, including the ionization of recollion-induced doubly excited states, the recollion-excitation with subsequent field ionization and the simultaneous emission upon rescattering. Then we show the typical characteristics of two-electron momentum distribution of different NSDI mechanisms, which give suggestions on experimental study of NSDI.