The problem of determining a set of system parameters that ensure a desired system output is of great interest for various applications such as in model validation/ invalidation and Quality-by-Design. This paper presents methods to construct an allowable box parameter set for system models expressed in a linear fractional form. The approaches are based on the structured singular value, μ, whose upper and lower bounds can be computed in polynomial time. It is shown that the problem of determining a parameter box as well as its center and/or shape can be reformulated as a constant-matrix μ-synthesis problem. A numerical example shows that the proposed methods successfully find the desired parameter boxes. The extension to ellipsoidal design space is also included.