The Oxford Thesaurus An A-Z Dictionary of Synonyms - besiege v.

1) lay siege to, beleaguer: For ten years Troy was besieged by the Greeks. 2) blockade, block, block off or up, hem in, cut off; surround, crowd round: The strikers have besieged the factory gates, not allowing anyone in or out. 3) importune, sue, petition, assail, pressurize or US pressure, press, overwhelm, inundate: The Home Office has been besieged by requests for leniency in your case.