A method and apparatus for conducting specific binding pair assays, such as immunoassays, is described. A porous membrane capable of non-bibulous lateral flow is used as assay substrate; a member of the binding pair is affixed in an indicator zone defined in the substrate. The sample is applied at a position distant from the indicator zone and permitted to flow laterally through the zone; any analyte in the sample is complexed by the affixed specific binding member, and detected. A novel method of detection employs entrapment of observable particle in the complex. Blood is a particularly preferred sample as the red blood cells can be used as the observable particles for detection of the complex.