A self-sealing male connector (20) includes a tubular male body (30) and an elastomericresilient tip (38) disposed on the distal end (50) of the tubular male body. Theelastomeric tip has a transverse size (44) that is greater that the size of a femaleconnector (42) and a shape that differs from the female shape so that engagementof the two will result in reshaping the male tip to the shape of the female flow channeland the male will create a seal with the channel. The male tip is formed with a slit(40) and a hollow core (56) that provides a flow passage formed in the male body.As the male tip is reshaped due to engagement with a female connector, the slitopens to establish fluid flow through the male connector. In one embodiment,the transverse shape of the male tip is elliptical having a major axis (46) alongwhich the slit is formed. In one embodiment, the male tip is oversized in all transversedimensions and forms an edge seal with the female connector at first contact.The proximal end (52) of the male connector may be configured as a conventionalfemale connector, a blood collection device (122) , or other. The male body canhave a Luer shape.