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The Inertia Relief (IR) technique is widely used by industry and produces equilibrated loads allowing to analyze unconstrained systems without resorting to the more expensive full dynamic analysis. The main goal of this work is to develop a computational framework for the solution of unconstrained parametric structural problems with IR and the Proper Generalized Decomposition (PGD) method. First, the IR method is formulated in a parametric setting for both material and geometric parameters. A reduced order model using the encapsulated PGD suite is then developed to solve the parametric IR problem, circumventing the so-called curse of dimensionality. With just one offline computation, the proposed PGD-IR scheme provides a computational vademecum that contains all the possible solutions for a predefined range of the parameters. The proposed approach is nonintrusive and it is therefore possible to be integrated with commercial finite element (FE) packages. The applicability and potential of the developed technique is shown using a three-dimensional test case and a more complex industrial test case. The first example is used to highlight the numerical properties of the scheme, whereas the second example demonstrates the potential in a more complex setting and it shows the possibility to integrate the proposed framework within a commercial FE package. In addition, the last example shows the possibility to use the generalized solution in a multi-objective optimization setting. K E Y W O R D Sinertia relief, nonintrusive, proper generalized decomposition, reduced order model, shape optimization INTRODUCTIONUnconstrained structures are widespread in the automotive, aerospace and naval industry. As is well known, due to the singularity of the stiffness matrix, conventional static analyses cannot be performed if the system undergoes rigid body motions. At the same time, imposing dummy constraints in order to make a free-body system statically determinate leadsThis is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.