The stationary interaction parameter between the plane surfaces of two identical, cylindrical, polyethylene disks has been measured with the pulsed neutron method. It was shown that it is possible to overcome the delay effect caused by the flight of the neutrons in the gap between the moderators through the insertion of absorbers. In the measurements the ratio of separation distance to diameter was varied between 0.06 and 0.77; the resulting values of the interaction parameter varied from 0.93 to 0.24. Two different thicknesses of the disks were employed; one assembly gave decay constants from 10 000 to 17 000 sec−1 and the other assembly yielded values in the range 17 000 to 40 000 sec−1. Although full equilibrium of the neutron distribution was not reached in all cases for the last series, the two series show a general agreement. A calculation based on a zero'th-order Bessel function as radial distribution and (cos θ)/π as angular distribution of the neutrons leaving the interacting surfaces gives a too-large interaction parameter for all separation distances. However, the overestimate is small when the surfaces are close together.