Propagation buckling mechanisms in pipe-in-pipe (PIP) systems with thin and moderately thin carrier pipes with a diameter-to-thickness (Do/to) ratio in the range 26–40 are investigated using 2D analytical and 3D nonlinear (material and geometry) finite element (FE) models. The FE models are validated against hyperbaric chamber tests of a PIP system with Do/to of 30. Using the validated FE model a parametric study is conducted and two distinct buckle propagation modes in PIPs are observed. Empirical expressions for each mode are proposed and are found to be different from previous expressions suggested for PIPs with (Do/to) ratio in the range 15–25.