The influence of longitudinal constructive discontinuity on the stability of the plate in the domain of elastic stability is solved based on the classical thin plate theory. The constructive discontinuities divide the plate into fields of different thickness. The plate has two opposite edges simply supported while the other two edges can take any combination of free, simply supported and clamped conditions. The Levy method is used for the solution of the problem of stability, with the aim of developing an analytical approach when researching the stability of plates with longitudinal constructive discontinuities and also with the aim of obtaining exact solutions for plates with non-uniform thickness. The exact solutions for stability presented herein are very valuable as they may serve as benchmark results for researches in this area