Abstract： A well-structured pushdown system(WSPDS) is a pushdown system equipped with well-quasi-order states and a well-quasi-order stack alphabet. It is shown that several extensions of vector addition systems can be reduced to a WSPDS. By applying post-order calculation of its derivation tree, the branching vector addition system can be encoded to some WSPDS. The recursive vector addtion system is a special class of WSPDS if a stack is explicitly introduced to its transitions. The vector addtion system with one zero-test can be encoded to some WSPDS where the depth of the stack represents the dimension for zerotest. These results exhibit the powerful expressivenss of WSPDS.