The two-dimensional steady heat flow in bodies with different cross-sections and isothermal boundaries is a problem that has been investigated intensively in the literature. For the cross-section of two concentric circles the analytical solution of the shape factor as a function of the ratio of the outer diameter to the inner diameter is well known and can be found in most textbooks on heat transfer. For some simple well defined geometries it is possible to calculate the shape factor by the method of conformal mapping. But for arbitrarily shaped cross-sections numerical methods or correlations fitted to measured or calculated values have to be used. We applied the Method of Finite Elements and the Method of Finite Differences to calculate shape factors for cross-sections bounded by concentric circles and squares. By developing the shape factor for the investigated cross-sections analytical approximations for the shape factor are obtained. The approximations fulfil limiting cases and are close to the exact solutions when being fitted to the numerical values.