The invention includes antibodies or antigen-binding fragments thereof which bind specifically to conformational epitopes on the extracellular domain of PSMA, compositions containing one or a combination of such antibodies or antibodies or antigen-binding fragments thereof, hybridoma cell lines that produce the antibodies, and methods of using the antibodies or antigen-binding fragments thereof for cancer diagnosis and treatment. The invention also includes oligomeric forms of PSMA proteins, compositions comprising the multimers, and antibodies that selectively bind to the multimers.