  We derive a one-dimensional (1d) model for the analysis of bulging or necking
in an inflated hyperelastic tube of {\it finite wall thickness} from the
three-dimensional finite elasticity theory by applying the dimension reduction
methodology proposed by Audoly and Hutchinson (J. Mech. Phys. Solids, 97,
2016). The 1d model makes it much easier to characterize fully nonlinear
axisymmetric deformations of a thick-walled tube using simple numerical schemes
such as the finite difference method. The new model recovers the diffuse
interface model for analyzing bulging in a membrane tube and the 1d model for
investigating necking in a stretched solid cylinder as two limiting cases. It
is consistent with, but significantly refines, the exact linear and weakly
nonlinear bifurcation analyses. Comparisons with finite element simulations
show that for the bulging problem, the 1d model is capable of describing the
entire bulging process accurately, from initiation, growth, to propagation. The
1d model provides a stepping stone from which similar 1d models can be derived
and used to study other effects such as anisotropy and electric loading, and
other phenomena such as rupture.
