A biaxially drawn polyester vessel having good resistance to heat distortion and gas-barrier properties, which is prepared by biaxially draw-blow forming of a preform comprising inner and outer layers of a polyester composed mainly of ethylene terephthalate units and at least one intermediate layer composed of a gas-barrier resin with the temperature conductivity of the gas-barrier resin being 1/2 to 1/3 the temperature conductivity of the polyester, wherein the barrel of the vessel has pillar convexities having a relatively large diameter and a short circumference and panel-like concavities having a relatively small diameter and a long circumference, which are alternately arranged in the circumferential direction of the barrel where the circumferential size of the panel-like concavities is 10 to 50 mm, the axial size of the panel-like concavities is 40 to 160 mm and the step between the panel-like concavities and the pillar convexities is 1 to 8 mm, the panel-like concavities having a function of expanding and contracting in the diameter direction of the barrel according to the change of the pressure in the vessel, the inner and outer layers in the panel portion are biaxially and molecularly oriented so that the in-plane orientation degree (l+m) is at least 0.350, and the inner and outer layers in the panel portion are heat-set so that the crystallization degree, determined by the density method, of the outer layer in the panel portion is at least 30% and is higher by at least 2% than the crystallization degree of the inner layer in the panel portion.