A class of anionic oligomers and polymers that function for inhibition of nucleases, particularly RNase. Specific inhibitors include mixtures of oligomers of vinyl sulfate. Methods for inhibition or inactivation of one or more nucleases in vitro which comprises the step of contacting the one or more nucleases in a biological medium with one or more of the anionic oligomeric or polymeric inhibitors of this invention. Kits for carrying out a biological procedure, biological reaction and/or a biological assay containing one or more inhibitors of this invention. The use of oligomers and/or polymers of this invention as additives in buffers or reagents. The inhibitors of the invention can also be attached to surfaces to provide for removal of nucleases from media, solutions or other liquids in contact with the solid.