  The buckling of hyperelastic incompressible cylindrical tubes of arbitrary
length and thickness under compressive axial load is considered within the
framework of nonlinear elasticity. Analytical and numerical methods for
bifurcation are developed using the exact solution of Wilkes for the linearized
problem within the Stroh formalism. Using these methods, the range of validity
of the Euler buckling formula and its first nonlinear corrections are obtained
for third-order elasticity. The values of the geometric parameters (tube
thickness and slenderness) where a transition between buckling and barrelling
is observed are also identified.
