An analytical theory is presented for the generation of small-amplitude three-dimensional monochromatic internal waves by an oscillating object. The theory expresses the structure of the waves in terms of the size of the object, the viscosity of the fluid and the time elapsed since the start-up; to this, it adds near-field effect and modification of the added mass of the object by the stratification. Comparison with experiment allows assessment of the relative importance of all five effects.