The details on breakup processes of liquid column and sheet are numerically investigated to provide the physics of the capillary instabilities and formation of liquid drops. Two cases are used: A numerical analysis on the capillary instabilities and breakup processes of a cylindrical liquid column and a moving liquid sheet in a moving gaseous medium to analyze the dynamics and breakup of the liquid sheet. The problem, composed of the Navier-Stokes systems associated with surface tension forces, is solved by the Volume of Fluid (VOF) technique with a Continuum Surface Force (CSF) to artificially smooth the discontinuity present at the interface. The results show that before disintegration of the liquid the capillary waves become unstable and the source of making the wave unstable is inherently developed by the system. The investigation of moving liquid sheet showed that the two modes of forces for liquid stretching exists: shear force causing the stretching of liquid by shear velocity and drag force causing the stretching of liquid by gas velocity ahead of the tip of the liquid sheets. Stretching of liquid by shear force causes the protrusion of liquid from the tip of liquid sheet and the surface tension force causes the tip of the sheet to make it round. It can also be revealed that the aerodynamic force at the tip of the sheet plays an important role to continue the stretching of sheet and controls the formation of droplet with the occurrence of sheet breakup.