The thermal conductivities of two groups of silicon nanoribbons of ∼20 and ∼30 nm thickness and various widths have been measured and analyzed through combining the Callaway model and the Fuchs-Sondheimer (FS) reduction function. The results show that while the data for the ∼30 nm thick ribbons can be well-explained by the classical size effect, the measured thermal conductivities for the ∼20 nm thick ribbons deviate from the prediction remarkably, and size effects beyond phonon-boundary scattering must be considered. The measurements of the Young's modulus of the thin nanoribbons yield significantly lower values than the corresponding bulk value, which could lead to a reduced phonon group velocity and subsequently thermal conductivity. This study helps to build a regime map for thermal conductivity versus nanostructures' surface-area-to-volume ratio that clearly delineates two regions where size effects beyond the Casimir limit are important or not important.