This study focuses on dynamic buckling of functionally graded material (FGM) cylindrical shells under thermal shock. The transient non-uniform temperature fields in the FGM shells subjected to dynamic thermal loading are determined using an analytic method. Based on the Hamiltonian principle, the dynamic thermal buckling problem of the FGM cylindrical shells is transformed into the symplectic space for solving. At the same time, the buckling thermal loads and buckling modes corresponding to generalized eigenvalues and eigen solutions of canonical equations can be calculated via the bifurcation conditions. The dynamic thermal buckling characteristics of the FGM cylindrical shells as well as the solving processes are given by the symplectic method. A complete dynamic buckling modes space is presented for the FGM cylindrical shells. The effects of the material gradient, parameters of structural geometry and thermal loadings on the dynamic buckling temperature are discussed. © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.