An apparatus for accurately infusing fluids into a patient at specific rates over an extended period of time. The apparatus is of a low profile, laminate construction having a stored energy source in the form of a distendable membrane, which in cooperation with the base of the apparatus defines one or more fluid reservoirs each having a fluid inlet and a fluid outlet. The apparatus further includes a novel, conformable ullage made of formable materials. The conformable ullage uniquely conforms to the shape of elastomeric membrane as the membrane returns to its less distend configuration and in so doing can move between a central chamber and a toroidal chamber formed in the cover of the apparatus. This arrangement will satisfy even the most stringent medicament delivery tolerance requirements and will elegantly overcome the limitations of materials selection encountered in devices embodying solely rigid ullage construction. Additionally, the infusion cannula of the apparatus is connected to the base in a novel manner which permits expeditious subdermal delivery to the patient via a cannula which extends generally perpendicularly relative to the base.