Interest in elasticity estimation for thin layers is increasing because of the various potential applications, including dermatology and cosmetology. In this context, we propose a dedicated elastographic system using 1-D high-frequency transient elastography (HF-TE) to estimate the 1-D Young's modulus through the dermis and hypodermis, which are the two human skin layers of interest in this study. An experimental validation of the HF-TE method was first carried out on two homogeneous tissue-mimicking hard and soft phantoms. The Young's modulus values obtained in these phantoms were compared with those obtained by two complementary shear wave propagation techniques: shear wave-induced resonance elastography (SWIRE) and supersonic shear imaging (SSI). A third two-layer thin phantom, with mechanical properties similar to those of skin, was used to validate the ability of HF-TE to distinguish layers and measure elasticity. Finally, preliminary in~vivo experiments conducted on forearm and cheek skin revealed the promising performance of HF-TE in measuring elasticity in the dermis and hypodermis.