A multi-seal flexible recloseable package having a tapered product cavity formed in one of the package sidewalls has a generally wedged-shaped cavity into which a doubled-over shingled stack of the food product slices are sealed. The package has a first, peelable hermetic seal located next to an access edge of the product cavity and a second, recloseable seal positioned directly above the peelable seal. Vertical extensions of the package sidewalls are sealed together at their tops to form a third package seal which has a tamper-evident tear strip. One or more openings in the vertical package extensions allow the package to be supported on a display hook.