The numerical modeling of viscous drops and films have been restrictive due to the difficulty in solving the full transport equations where the location of the boundary is not knowna priori, and also due to the perplexity in calculating an accurate surface curvature. In this paper we combine an advanced numerical algorithm (FLAIR) with a newly presented and accurate curvature calculation scheme, to study the dynamics of viscous drops and films. It is demonstrated that this technique can resolve the complex flow fields and large surface deformations of the type which are common in studies of viscous liquid drops and films. The evolution of the shape and internal flow field of an initially elliptic, infinitely long, viscous liquid cylinder and a liquid film with both symmetric and asymmetric large amplitude sinusoidal surface disturbances are calculated numerically.