A manually operated mechanical pump for drug infusion through a syringe including a plunger slidable within a syringe body to cause drug contained within the syringe body to exit a front opening of the syringe. The pump has a pump body with an open front end, to which the syringe attaches, and an open rear end, at which a drive member is associated movably relative to the pump body. A pair of thrust members are provided between the drive member and the syringe to impart longitudinal thrust in a distal direction onto the plunger to cause the drug to exit the front opening. An elastic element is provided between the thrust members to store and release elastic energy when the first thrust member proximal to the drive member is manually actuated, thus causing the second thrust member proximal to the syringe to advance as the drug exits the front opening.