A model is presented in which the sintering behavior of a ceramic film which is constrained by a rigid substrate is contrasted with the sintering behavior of a free film. The problem is made simple by the assumption that the stress field developed in the film is uniform. This simplification allows several closed form solutions to be obtained. The solutions give new insights into the sintering behavior of films supported on a substrate. It is found (1) that the shear rate of the film is more important in the sintering process than its densification rate when the film is constrained by a substrate, (2) that the incompatibility stress is time dependent and reaches its maximum value during the initial stages of sintering, (3) that the magnitude of that maximum stress may be tensile or it may be compressive depending on the shear response of the material, and (4) that if the incompatibility stress is tensile it can lead to the formation of cracks or defects in the ceramic film.