Methods of administering glyburide, or other drug, are disclosed. The novel methods disclosed herein include intravenous methods of administering glyburide, or other drug, over periods of more than an hour, preferably over periods of about 72 hours. The novel methods include administering a bolus of glyburide, or other drug, followed by a first continuous infusion administration of glyburide, or other drug; and optionally a second or further bolus administration of glyburide, or other drug, and/or a second or further continuous infusion administration of glyburide, or other drug. These methods are effective to rapidly achieve a desired level of glyburide, or other drug, and to provide a substantially steady level of glyburide, or other drug, over a desired period of time. The methods disclosed herein may be useful for treating a subject in need of treatment for, e.g., acute stroke (ischemic and hemorrhagic), traumatic brain injury (TBI), spinal cord injury (SCI), myocardial infarction (MI), shock (including hemorrhagic shock), organ ischemia, and ventricular arrhythmias. These methods provide for the rapid achievement and maintenance of therapeutic glyburide, or other drug, plasma levels over an extended period of time, and further avoid excessive levels of drug and so avoid possible drug side-effects.