Abstract: Based on large deformation geometrical relations, a mathematical model described with differential algebraic equations is presented for axisymmetric hyperbolic thin-metal shells with variable thickness under internal pressure, which remedies the low precision in solving finite strain problems based on Gleyzal’s geometrical relations expanded with Taylor’s formula. Numerical solutions are carried out using Klopfenstein-Shampine numerical differentiation formulae with varying step size and order. The distributions of stresses, strains, and displacements of metal shells at specific moments can be obtained. Numerical solutions by the proposed model and the Gleyzal’s model were compared with experiments. The results show that the proposed model can give more objective results in the finite strain analysis of bulged hyperbolic thin-metal shells.