In this contribution elastic stability of an eccentric circular annulus is treated. The central wall plane was placed in a complex number plane ($z$) and conformally mapped onto an eccentric circular annulus of a complex number plane $(\zeta)$. With the help of the differential method and the IBM 1130 computer, the buckling coefficients are defined numerically in this way for a wall that is cantilevered from both sides and which is characterized by uniform compressive stress $(P_N=P_Z<0)$ on both edges or by uniform compressive stress $(P_N=0)$, $(P_Z<0)$ is only loaded on the outer edge. The results and deviations are shown in the tables and diagrams.