In the paper, the authors present the shakedown analysis of the plate structures pre-loaded beyond the elastoplastic range. Two cases of loading are considered, namely: the structure is subjected to the action of two independent sets ofloads with constant points of application or one parameter set of loads moves slowly according to an a priori described program. As a result, the safe loading boundary or the shakedown load parameter are calculated, respectively, by means of the finite element method (FEM). Three examples confirmed the effectiveness of the proposed algorithms of analysis.