We report the first Monte Carlo simulations of the morphology of asymmetric diblock copolymer thin films confined between two homogeneous and identical surfaces. The copolymers form a cylindrical morphology; in the bulk. Exploratory bulk simulations have been conducted with judicious choices of the simulation box dimensions to find the characteristic periodicity of the cylinders. The morphological dependence of the thin films on the surface-block interactions and the film thickness has then been systematically investigated, Our results are in good agreement with experimental observations.