The paper deals with the problem of the local buckling caused by uniaxial stretching of an infinite plate with a circular inclusion from a different material. The effect of elastic modulus of the inclusion on the value of the critical load is investigated. In order to find the first critical load a variational principle is applied. The comparison of numerical results that were obtained in the Maple 18 and the results obtained by the finite element method in the ANSYS 13.1. The influence is analysed the ratio of the elastic properties of the inclusion and plate on the value of the critical load and the form of the loss of stability.