The present teachings are directed to a modular shoulder prosthesis having an adjustable radial offset and/or angular inclination provided by relative rotation of an adapter interdisposed between the stem and the head. In one example, a shoulder prosthesis comprises a stem having a first longitudinal axis. The shoulder prosthesis can also include an adaptor including a first taper. The first taper can have a first taper axis. The shoulder prosthesis can include a head rotatably supported by the adaptor. The head can have a semi-spherical articulating surface. The head can be coupled to the first taper and can be positionable relative to the stem through rotation of the adaptor about the first taper axis for adjusting an offset of the head relative to the longitudinal axis of the stem.