The present invention relates to an improved system for efficiently and accurately performing immunoassays, such as ELISAs. The invention provides an immunoassay assembly which includes a flow-through unit and an aspiration pump. The immunoassay flow-through unit includes an outer seal; at least one bed support; an inner seal; and a packed non-porous bed. The unit is releasably attached to an aspiration pump which enables the controlled flow rate of liquid passing through the packed bed of the flow-through unit. The invention also provides a method of using the immunoassay assembly to identify analytical targets of interest.