  We study monogamy relations for arbitrary dimensional multipartite systems.
Monogamy relations based on concurrence and concurrence of assistance for any
dimensional $m_1\otimes m_2\otimes...\otimes m_{N}$ quantum states are derived,
which give rise to the restrictions on the entanglement distributions among the
subsystems. Besides, we give the lower bound of concurrence for four-partite
mixed states. The approach can be readily generalized to arbitrary multipartite
systems.
