This study reports the discovery of elastic wave mode conversion, called the Transmodal Fabry-Perot Resonance. Unlike electromagnetic waves and acoustic waves, elastic waves have both longitudinal and transverse waves (i.e., shear wave) due to the atomic bonds in solids. When this newly-discovered resonance occurs, a longitudinal wave can be maximally converted to a shear wave through a certain type of anisotropic media. We discovered that this resonance occurs if two longitudinal-shear mode-coupled waves in an anisotropic layer have specific phase differences. Furthermore, we have succeeded in experimentally verifying the resonance mechanism using elastic metamaterials in the ultrasound frequency range. We believe that the new resonance phenomenon has a great potential in high-resolution and efficient ultrasound imaging because we can efficient generate difficult-to-generate shear-mode ultrasound.