The nonlinear viscous flow problem associated with a heaving vertical cylinder with two heave plates in the form of two circular disks attached is solved using a finite difference method. Numerical experiments are carried out to investigate the spanwise length effects on the hydrodynamic properties, such as added mass and damping coefficients. Over a Keulegan-Carpenter (KC) number range from 0.1 to 0.6 at frequency parameter (beta = 7.869 X 10^7), calculations indicate that a KC-dependent critical value of spanwise length L/D_d (L - the distance between the disks, and D_d - the diameter of the disks) exists. A significant influence of L/D_d on the vortex shedding patterns around the disks and the hydrodynamic coefficients is revealed when L/D_d is smaller than the critical value due to strong interaction between vortices of different disks. Beyond that limit, however, both added mass and damping coefficients are shown to be rather stable, indicating the independence of the vortex shedding processes of different disks.