Considered is an elastic, incompressible, isotropic material whose constitutive law is specified by a strainenergy function W which is a function of two strain invariants I sub 1 and I sub 2. In the mathematical theory of large deformations of axially symmetrical elastic mem branes, the governing equations are a set of nonlinear ordinary differential equations. Three types of deformation of thin circular cylindrical rubber tubes are discussed. In the first type a rubber tube is deformed into another circular cylindrical tube of different length and diameter by simultaneous inflation and extension of the tube. The second type of deformation considered is a stretching of the tube without internal pressure. The third type is a tube inflated by internal pressure, with or without a change in total length or end diameter. In these two types the deformed tube is a curved surface of revolution the analysis is more complicated, and the calculations are restricted to Mooney-Rivlin materials.