Abstract: A ballistics vest of the soft body armor type comprises multiple overlying layers of a thin, flexible fabric made of woven plastic fibers secured together to form a soft, flexible front panel located on a strike side of the vest, and multiple overlying layers of a thin, flexible imperforate plastic sheet stacked behind the flexible front panel, on a body side of the vest. The flexible plastic sheets preferably comprise an array of plastic fibers embedded in a resinous matrix that forms the sheet material. The flexible front panel and the stack of flexible plastic sheets behind it have a combined areal weight not greater than about 1.20 lbs/ft.sup.2 and have an NIJ Standard maximum backface of about 44 mm with a ballistics resistance that successfully prevents projectile penetration of the combined stacks of flexible layers according to NIJ Standard 0101.03 for Threat Level IIIA.