Photodesorption of CO ice is suggested to be the main process that maintains a measurable amount of gaseous CO in cold interstellar clouds. A classical molecular dynamics simulation is used to gain insight into the underlying mechanism. Site-site pair potentials were developed on the basis of ab initio calculations for the ground and excited nonrigid CO dimer. Both amorphous and crystalline CO dusters were created and Characterized by their densities, expansion coefficients, binding energies, specific heats, and radial distribution functions. Selected CO molecules were electronically excited With 8.7-9.5 eV photons. CO returns to the ground state after a finite lifetime on-the excited potential surface. Two desorption mechanisms ate found: (1) direct desorption where excited CO itself is released from the cluster the landing on the ground state in an unfavorable orientation; (2) "kick-out" desorption where excited CO kicks out a neighboring CO molecule: These findings are in accord with laboratory experiments. Little dependence on size of the cluster, excitation energy and temperature in the 6-18 K range was found. The predicted photodesorption probability is 4.0 x 10(-3) molecules photon(-1), smaller by a factor of 3-11 than that given by experiments.