A method of making a three-dimensional object is carried out by: (a) providing an apparatus comprising a radiation source, a carrier on which the three dimensional object is made, and a movable belt positioned therebetween, the belt having a first surface and an opposite second surface, with the belt comprised of an optically transparent material, and with the belt permeable to a polymerization inhibitor; (b) applying a polymerizable liquid to the first surface of the belt, and contacting the second surface of the belt to the polymerization inhibitor, (c) contacting a portion of the belt first surface having the polymerizable liquid thereon to the carrier or the three dimensional object so that the belt adheres thereto with the polymerizable liquid positioned therebetween; (d) irradiating the polymerizable liquid with actinic radiation through the belt from the radiation source to polymerize the polymerizable liquid positioned therebetween; then (e) optionally separating the belt from the carrier or the three dimensional object; and then (f) repeating steps (b) through (e) until the three dimensional object is completed. Apparatus for carrying out the method is also described.