The dynamics of a viscoelastic Maxwell fluid is studied in a partially filled cylinder rotating around a horizontal axis. At low rotational velocity, the fluid behaves in the same manner as a viscous fluid. A thin fluid film is pulled up from the edge of a fluid bump at the bottom of the cylinder, and it covers the inner wall of the cylinder completely. As a result, a steady state is the coexistence of the film and the bump of the fluid. When the rotational velocity of the cylinder is increased, the film formation fails and the bump of fluid rolls steadily at the bottom of the cylinder. This failure of film formation has never been observed in the case of a viscous fluid. At higher rotational velocity, the bump of the fluid starts to oscillate at the bottom of the cylinder. Then, the fluid bump again rolls steadily with a further increase in the rotational velocity. The failure of film formation is explained in terms of the elastic behavior of the viscoelastic fluid near the boundary between the film and the bump regions. The theoretical prediction shows good agreement with the experimental results. We further estimate the condition for which a viscoelastic fluid displays dynamically nonwetting behavior; i.e., the absence of fluid film at any value of rotational velocity.