In multibody dynamics, differential and algebraic equations which can satisfy both equation of motion and kinematic constraint equation should be solved. To solve this equation, coordinate partitioning method and constraint stabilization method are commonly used. The coordinate partitioning method divides the coordinate into independent and dependent coordinates. The most typical coordinate partitioning method are LU decomposition, QR decomposition, projection method and SVD(sigular value decomposition). The objective of this research is to find a efficient coordinate partitioning method in flexible multi body systems and a hybrid decomposition algorithm which employs both LU and projection methods is proposed. The accuracy of the solution algorithm is checked with a slider-crank mechanism.