Wrinkling is a phenomenon associated with problems of stability. Although being an unwelcome occurence on macroscale examples, potential use can be found on the microscale. Quite a few models describing wrinkling have been developed, yet few give simple, analitically solvable expressions for determining the properties of wrinkling. Such relations are possible for configurations with simple geometries and stress distributions. One such example is analysed in this work. We investigate wrinkling of a circular film on a substrate, evenly loaded at the edge. A mathematical model for wrinkling of thin circular plates, which is based on von Kármán plate theory, is derived as a tool for predicting its mechanical properties. The general differential equation is derived, from wich the stability equation and the expression for the critical stress follow. The model's predictions and results are then compared with simulations that were done in Abaqus. We run a few simulations where we vary the thickness of the plate and its Young's modulus. Some differences are found between the results obtained from the model and the simulations.