Tapering in laminated composites is introduced by terminating plies called ply drop-off. Strength reduction in such materials is caused by delamination failures and matrix cracks that occur at terminating plies. Tapering composite is generally designed based on many test results and empirical rules. The failure load and mode at ply drop-off can be changed depending on the type of material and shape, so many tests are needed for adequate design. The failure modes of various ply drop-offs were revealed and a progressive failure analysis was proposed to decrease the number of trial-and-error tests in this study. The proposed method was based on constitute damage mechanics (CDM) for inplane failure and cohesive zone modeling (CZM) for interlaminar failure. The lamina behaviors were incorporated into the versatile finite element software Abaqus with a user subroutine developed by the authors. The analysis corresponding to the tests showed that progressive failure analysis could predict the failure loads and modes.