Method for manufacturing a laminated trim part by covering a three-dimensional substrate with a skin applied by lamination under vacuum or by suction, said part having at least one particular peripheral substrate portion which is not covered by said skin , said method being characterized in that it consists in: providing a substrate support with a bearing surface exhibiting a form conjugate to that of the face of the substrate that is opposite to the face to be covered, and which is provided with a lower part of a peripheral clamping or pinching frame surrounding said support , but beyond which there projects from beneath at least one specific lateral support portion , disposing the substrate to be covered on the support such that said at least one particular peripheral substrate portion rests on said at least one specific lateral support portion , providing a section of skin of a size adapted to the frame , providing a thermo-adhesive or cold-bonding adhesive substance which is added to the substrate or to the rear face of the skin , disposing said skin , where appropriate after heating, on the substrate mounted on the support , with interposition of the layer of adhesive substance and such that it laterally projects beyond the lower frame part over the entire circumference of the latter, providing and supplying an upper clamping or pinching frame part (6"), of complementary form to the lower frame part , pinching the skin in an airtight manner between the two mutually cooperating, complementary frame parts (6' and 6"), generating an aspiration or suction effect through the substrate so as to intimately apply that part of the section of skin that is located inside the frame against the substrate , moving the upper frame part (6") away, possibly after a predetermined time has elapsed, and withdrawing the part formed by the substrate partially covered by the skin , and cutting off, where appropriate, the portions of the skin that are not secured to the substrate . providing a substrate support with a bearing surface exhibiting a form conjugate to that of the face of the substrate that is opposite to the face to be covered, and which is provided with a lower part of a peripheral clamping or pinching frame surrounding said support , but beyond which there projects from beneath at least one specific lateral support portion , disposing the substrate to be covered on the support such that said at least one particular peripheral substrate portion rests on said at least one specific lateral support portion , providing a section of skin of a size adapted to the frame , providing a thermo-adhesive or cold-bonding adhesive substance which is added to the substrate or to the rear face of the skin , disposing said skin , where appropriate after heating, on the substrate mounted on the support , with interposition of the layer of adhesive substance and such that it laterally projects beyond the lower frame part over the entire circumference of the latter, providing and supplying an upper clamping or pinching frame part (6"), of complementary form to the lower frame part , pinching the skin in an airtight manner between the two mutually cooperating, complementary frame parts (6' and 6"), generating an aspiration or suction effect through the substrate so as to intimately apply that part of the section of skin that is located inside the frame against the substrate , moving the upper frame part (6") away, possibly after a predetermined time has elapsed, and withdrawing the part formed by the substrate partially covered by the skin , and cutting off, where appropriate, the portions of the skin that are not secured to the substrate . <EOS>