Analytical compliance model is vital to the flexure-based compliant mechanism in its mechanical design and motion control.The matrix is a common and effective approach in the compliance modeling while it is not well developed for the closed-loop serial and parallel compliant mechanisms and is not applicable to the situation when the extemal loads are applied on the flexure members.Concise and explicit analytical compliance models of the serial flexure-based compliant mechanisms under arbitrary loads are derived by using the matrix method.An equivalent method is proposed to deal with the situation when the extal loads are applied on the flexure members.The extal loads are transformed to concentrated forces applied on the rigid links,which satisfy the equations of static equilibrium and also guarantee that the deformations at the displacement output point remain unchanged.Then the matrix method can be still adopted for the compliance analysis of the compliant mechanism.Finally,several specific examples and an experimental test are given to verify the effectiveness of the compliance models and the force equivalent method.The research enriches the matrix method and provides concise analytical compliance models for the serial compliant mechanism.