Bree’s cylinder was used to show different material behaviors under constant mechanical and cyclic thermal gradient loadings. Bree showed different behaviors with the help of a diagram known by his name as Bree’s diagram. In this research, the problem was reconsidered without his simplified hypothesis. The used material model is nonlinear kinematic hardening. The two dimensional problem and the Poisson’s effect were considered. In order to obtain the Bree’s diagram, return mapping algorithm was used. The results showed that the one dimensional model of Bree is conservative and the bi-dimensional Bree’s diagram does not correspond to the complete model.