This paper provides an analytically tractable theoretical framework to study the optimal supply of central bank reserves when the demand for reserves is uncertain and nonlinear. We fully characterize the optimal supply of central bank reserves and associated market equilibrium. We find that the optimal supply of reserves under uncertainty is greater than that absent uncertainty. With a sufficient degree of uncertainty, it is optimal to supply a level of reserves that is abundant (on the flat portion of the demand curve) absent shocks. The optimal mean spread between the market interest rate and administered rates under uncertainty may be higher or lower than that absent uncertainty. Our model is consistent with the observation that the variability of interest rate spreads is a function of the level of reserves.