The breakup of thin planar liquid sheets due to the nonlinear growth of disturbances is determined. Conservation equations are derived using a control volume method and solved using MacCormack's predictor-corrector scheme. It is found that the size and geometry of ligaments, formed during breakup, vary with the Weber number. Antisymmetric waves, which spontaneously intensify at higher values of the Weber number, give rise to thin ligaments. At lower values of the Weber number antisymmetric waves formed initially get transformed into symmetric interfaces giving larger ligaments. The magnitude of the initial amplitude of the disturbances is shown to strongly influence the disintegration. The results are compared with experimental results obtained for thin water sheets and good agreement is demonstrated.