Uniaxially stretched high density polyethylene (HDPE), low density polyethylene (LDPE) and ultra-high molecular weight polyethylene (UHMWPE) were studied by positron annihilation lifetime spectroscopy (PALS). The pick-off annihilation lifetime of ortho-positronium (o-Ps) was progressively shortened by stretching. This shortening is due to development of anisotropy in sub-nm size open space (free volume) for o-Ps localization. Simple analysis by an extended Tao-Eldrup model suggests that the hole anisotropy is much less than the bulk anisotropy possibly due to structural relaxation. Correlation between the o-Ps relative intensity and lifetime points to one-stage deformation of LDPE and UHMWPE, and multiple-stage deformation of HDPE, respectively. A recently commercialized positron lifetime spectrometer, which permits PALS to be performed with a single specimen, was found to be applicable to stretched polymers.