The generalized Hooke’s law in cylindrical coordinates is presented in terms of directional moduli of elasticity and Poisson’s ratios. It is used in deriving a solution for long pressurized orthotropic tubes with closed ends. Two sets of equations are found; one set is applicable to the study of compressible materials and the other to incompressible materials. The distinction is also described in terms of the moduli of elasticity and Poisson’s ratios.