This paper is focused on determining the plastic collapse load of vessels which consist of an inner cylinder prestressed by a surrounding winding. This winding consists of a wire helically wound edge-to-edge in pretension in a number of layers around the outside of the inner cylinder. As a consequence, compression stresses are introduced in the cylinder, and the fatigue life of the vessel can be greatly increased. The ASME code, Section VIII - Division 3, provides the analytical equations for the stress calculation in wire-wound vessels under linear-elastic conditions (ASME, 2007). However, to obtain the plastic collapse load of the vessel, finite element method should be used. In this way, the main aim of this paper is to present a numerical procedure for the FE simulation of wire-wound vessels. For this simulation, it must be taken into account that the wire winding is a continuous process where every new layer is coiled around all previous deformed layers. Hence, a layer-by-layer numerical procedure which takes into account this continuous process during winding has been developed. Some examples are given to demonstrate the applicability of the procedure. Once the numerical procedure was validated, it was used to obtain (i) the maximum circumferential stress after winding, (ii) the initial plastic load, and (iii) the plastic collapse load. To obtain the plastic collapse load, an elastic perfectly-plastic material behaviour has been considered. Finally, the numerical results obtained for the plastic collapse load were obtained as a function of several ratios over a wide range, which take into account the cylinder thickness, the wire-wound thickness, the wire-wound pretension and the yield limit of the material.