A drug delivery capsule from which the delivery of the drug is driven by the osmotic infusion of moisture by the capsule from a physiological environment is provided with a delivery orifice which opens intermittently to achieve a pulsatile delivery effect. The wall in which the orifice is formed is constructed of an elastic material, preferably an elastomer, which stretches under a pressure differential caused by the pressure rise inside the capsule as the osmotic infusion progresses. The orifice is small enough that when the elastic wall is relaxed, the flow rate of drug through the orifice is substantially zero, but that when the elastic wall is stretched due to the pressure differential across the wall exceeding a threshold, the orifice expands sufficiently to allow the release of the drug at a physiologically beneficial rate.