The development of selective coffee harvesting technologies requires detailed knowledge of the geometrical, physical, and mechanical properties of the subsystems of the coffee bush, including the elastic properties of the substructures of fruit and the coffee bean, which are directly related to the selectivity problem. The elastic properties of the mesocarp–exocarp and bean are not described in the literature due to the difficulty of characterizing these locally, since measuring each component of the coffee fruit structure (mesocarp–exocarp and bean) is not an easy task. However, determining the elastic properties (of the mesocarp–exocarp and bean) could help create realistic simulations as an initial estimation for selective coffee harvesting studies. The present work aims to bridge the gap in the mechanical characterization of the sub-structures of the coffee fruits by assessing the elastic properties of the mesocarp–exocarp and bean. Indentation tests were performed on eighty Coffee arabica L. var. Castillo fruits and beans, which were previously classified into four ripening stages using fruit color data in the CIELab color space. Young’s modulus and indentation hardness of the mesocarp–exocarp structure and beans were calculated, applying the Oliver and Pharr indentation model and Hertz contact theory.