The caudal fins of adult zebrafish are supported by multiple bony rays that are laterally interconnected by soft interray tissue. Little is known about the fin's mechanical properties that influence the bending in response to hydrodynamic forces during swimming. Here, we developed an experimental setup to measure the elastic properties of caudal fins in-vivo by applying micro-Newton forces to obtain bending stiffness and a tensional modulus. We detected overall bending moments of 1.5 - 4x10−9 Nm2 along the proximal-distal axis of the appendage showing a non-monotonous pattern that is not due to the geometry of the fin itself. Surgical disruption of the interray tissues along the proximal-distal axis revealed no significant changes to the overall bending stiffness, which we confirm by determining a tensional modulus of the interray tissue. Thus, the biophysical values suggest that the flexibility of the fin during its hydrodynamic performance predominantly relies on the mechanical properties of the rays.