We theoretically study kinetics of a polymer threading through a pore embedded in a flat membrane. We numerically solve three coupled kinetic equations for the number n(1) of polymer segments in one side of the membrane and expansion factors of the polymer chain in each side of the membrane. We find the time evolution n(1)proportional tot(1/(1+nu)) at late stages and the translocation time tau(t) is scaled as tau(t)proportional ton(1+nu) for large number n of the polymer segments, where nu is the effective size exponent of the radius of gyration of the polymer. When the polymer is translocated into a region with a good solvent condition (nu=3/5), we obtain n(1)proportional tot(5/8) and tau(t)proportional ton(8/5).(C) 2004 American Institute of Physics.