A polymer is formed into the shape of a one-piece composite part and then solidified by curing, setting, hardening or otherwise solidifying the polymer to form a shaped polymer form having a shape that does not draw. Composite material is laid up on the form and solidified to from the composite part. The rigidity required of the form to lay up the composite part can he provided by operating in the polymer form's glassy state, forming the shaped polymer form with a hollow core and placing a rigid insert designed to draw inside the hollow core with the polymer form in its elastomeric state or through a combination of both. In its elastomeric state the form becomes pliable (without relaxing to a different memorized shape) and can he drawn out of the one-piece composite part. Because the shape of the form does not draw, the form deforms as it is drawn. If used, the rigid insert is drawn out prior to removing the shaped polymer form. Upon removal, the polymer form in its elastomeric state returns to its original shape. The form may be used once and thrown away or reused to form multiple composite parts of the same shape.