Examples of generalized Weyl algebras (GWA) include algebras such as \(U(\mathfrak{sl}(2,{\mathbb C}))\), \(U_q(\mathfrak{sl}(2,{\mathbb C}))\), and Weyl algebras, among many others. Their simple modules and indecomposable weight modules have been classified. On the other hand, the classification of indecomposable weight modules of higher rank GWA is wild in the general case. In this paper, the authors construct a notion of twisted higher rank GWA and study their simple weight modules in a torsion-free case. They begin with a definition of twisted higher rank GWA. They then give canonical simple weight modules (in the torsion-free case). Finally, via two examples, they examine an analogue between simple finite-dimensional Lie algebras and the support of simple weight modules of twisted higher rank GWA.