Electric field and magnetic field phasors are expanded into recently found vector spherical wave functions of a biaxial medium quantified by two anisotropy parameters. The medium is termed biaxial when the two anisotropy parameters are unequal, uniaxial when they are equal, and isotropic when both are unity. Such an expansion has been adopted previously to represent the field phasors inside a scatterer made of the chosen medium, but suspended in free space. In this paper, it is used in computing radiation of electric and magnetic current sources immersed in the chosen medium. The computed fields are valid everywhere, including near-zone and far-zone regions. Duality relations are derived between elementary sources in the chosen medium: point-electric-dipole source and point-magnetic-dipole source. Numerical results on isotropic, uniaxial, and biaxial cases for elementary sources show the evolution of electric field, magnetic field, and directivity pattern in relation to the anisotropy of the medium. In essence, beam shaping including stretching and compression along certain directions is possible upon orienting the dipole's axis with respect to a distinguished axis when the medium is uniaxial, or on varying both anisotropy parameters when the medium is biaxial. As an example for a nonelementary source, line-electric-dipole radiation is considered. With the dipole axis being fixed, steering the main lobes toward the dipole axis, as well as increasing/ decreasing the maximum directivity and beamwidth of main and side lobes is possible by the same aforementioned procedure applied for elementary sources.