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A sample‐size effect on spin wave auto‐oscillations under parallel pumping is studied experimentally in tangentially magnetized rectangular samples of yttrium‐iron garnet (YIG) films where one of the in‐plane sizes is varied. A previously developed one‐dimensional theoretical model of unstable collective oscillations in the system of parametrically excited spin waves is used to describe the mechanism of spin wave auto‐oscillations observed in YIG films. Our results show that the one‐dimensional model (that works well for YIG spheres) gives only qualitative description of the sample‐size effect in YIG films and the incorporation of the second finite size (film thickness) in this model is needed to achieve quantitative agreement with experiment in the film geometry.