In this talk, we discuss non-weight \(\mathfrak{sl}_{2}\) -modules that are free of finite rank over \(U(\mathfrak{h})\) where \(\mathfrak{h}\) denotes the Cartan subalgebra of \(\mathfrak{sl}_{2}\). In particular, I will present a classification of simple scalar-type \(U(\mathfrak{h})\) modules of rank 2 and introduce several families of simple finite-rank \(U(\mathfrak{h})\) -free modules. This talk is based on joint work with D. Grantcharov and K. Zhao.