The counting rate dependent shift of pulse height distributions in cylindrical (flow) proportional counters has been studied. The effects of various counter tube constructional and operational parameters on this shift were investigated. Certain of these parameters also introduce time dependent features into the shift phenomenon. Space charge effects are not major causes of the shifts except under extreme operating conditions. Direct intervention of adsorbed molecules or molecular ions in the multiplication process may also be eliminated as major factors. It is hypothesized that the primary mechanism for the shift is the buildup on the anode wire of a loosely adherent sheath of polarizable molecules or molecular fragments of quench gas, which effectively increases the diameter of the anode wire, thereby decreasing the gas gain for a fixed applied voltage. The equilibrium thickness of the sheath is a function of counting rate, photon energy, gas gain, gas pressure, and wire diameter and surface condition. Calculation of the thickness of this sheath gives a reasonable result. By proper choice of anode wire diameter, material, and heat treatment, the shift can be made negligible. There is also some hope that a proper choice of quench gas can also reduce or eliminate the effect.