Surgical retrieval devices (10,110,160,170,180,200,220,330,401,501) for capturing tissues and fluids in endoscopic and laproscopic operations include a semi-rigid, resiliently collapsible and expandable basket (12,112,312,412) comprising a structural combination of resilient, semi-rigid snare wire (31,32,131,132,531,532) and frame wire members (33,34,35,36,37,133,134,135,136,137,437) that are formed with a yieldable bend configuration that together flare into a basket form when extended out of a catheter (16). The basket is enhanced by surrounds of net, mesh, or impervious material (162,172,202,222,302,420) for retaining smaller bits of tissue or fluids, or with a web of interspersed flexible threads (60,184) for enhanced tissue retaining capability.