We present a list of 13 candidate gravitationally lensed submillimeter galaxies (SMGs) from 95 square degrees of the Herschel Multi-tiered Extragalactic Survey, a surface density of 0.14±0.04deg^{-2}. The selected sources have 500um flux densities (S_500) greater than 100mJy. Gravitational lensing is confirmed by follow-up observations in 9 of the 13 systems (70%), and the lensing status of the four remaining sources is undetermined. We also present a supplementary sample of 29 (0.31±0.06deg^{-2}) gravitationally lensed SMG candidates with S_500=80--100mJy, which are expected to contain a higher fraction of interlopers than the primary candidates. The number counts of the candidate lensed galaxies are consistent with a simple statistical model of the lensing rate, which uses a foreground matter distribution, the intrinsic SMG number counts, and an assumed SMG redshift distribution. The model predicts that 32--74% of our S_500>100mJy candidates are strongly gravitationally lensed (mu>2), with the brightest sources being the most robust; this is consistent with the observational data. Our statistical model also predicts that, on average, lensed galaxies with S_500=100mJy are magnified by factors of ~9, with apparently brighter galaxies having progressively higher average magnification, due to the shape of the intrinsic number counts. 65% of the sources are expected to have intrinsic 500micron flux densities less than 30mJy. Thus, samples of strongly gravitationally lensed SMGs, such as those presented here, probe below the nominal Herschel detection limit at 500 micron. They are good targets for the detailed study of the physical conditions in distant dusty, star-forming galaxies, due to the lensing magnification, which can lead to spatial resolutions of ~0.01" in the source plane. ; Comment: ApJ in press. 31 pages, 16 figures, 5 tables. This version updated to match accepted version