Loss of stability under uniaxial tension in an infinite plate with a circular inclusion made of another material is analyzed. The influence exerted by the elastic modulus of the inclusion on the critical load is examined. The minimum eigenvalue corresponding to the first critical load is found by applying the variational principle. The computations are performed in Maple and are compared with results obtained with the finite element method in ANSYS 13.1. The computations show that the instability modes are different when the inclusion is softer than the plate and when the inclusion is stiffer than the plate. As the Young's modulus of the inclusion approaches that of the plate, the critical load increases substantially. When these moduli coincide, stability loss is not possible.