Two different kinds of heterogeneous elastic hollow cylinders are studied in the present paper. One is a multi-layered cylinder with different values in different layers for both elastic modulus and Poisson's ratio. Another is an elastic hollow cylinder with continuously graded material properties. By introducing two recursive algorithms, the extrusion stresses between two neighbor layers in the multi-layered cylinder submitted to uniform pressures on the inner and outer surfaces can be simply determined. Then the exact solutions of the multi-layered structure can be found based on Lame ยด's solution.
For the hollow cylinder with continuously graded properties, the displacement method is used. Both Whittaker equation and hyper-geometric equation are derived and successfully solved, and then the exact solutions are found. The results obtained in the present paper are compared with the numerical solutions and good agreements are found. At the end of the present paper, some inherent properties of these two different kinds of heterogeneous elastic hollow cylinders are presented and discussed. The results obtained in the present paper are useful in the design and analysis for composites reinforced by unidirectional fiber layers.