The energy stored in an extended elastomeric reservoir can be usefully employed in the controlled delivery of drug solutions at constant rates of flow through a fixed resistance. The absolute level and constancy of pressure presented to the upstream end of the flow restrictor can be related, respectively, to the geometry and composition of the elastomeric reservoir. (The reservoir is to contain, in its distended form, the volume of drug to be delivered to the human venous system.) It has been established that the defining criteria for minimizing static pressure loss in the reservoir and for maintaining constancy of pressure through most of the delivery interval are stress decay and hysteresis, as measured in uniaxial stress-strain testing. The elastomeric composition most successfully meeting these requirements has been found to be non-reinforced isoprene rubber, crosslinked with a peroxide.