We carried out a numerical dosimetry study for in vitro experiments on millimetre-wave (MMW) biological effects on cells. The cell layers are cultured in 35 mm Petri dishes placed in the far-field region of a rectangular horn irradiator generating a 50.0 GHz continuous sinusoidal MMW. The finite-difference time-domain (FDTD) method and the second-order approximation of the absorbing boundary conditions (ABCs) are applied in calculating the specific absorption rate (SAR) in the cells. The 0.125 mm and 0.25 mm voxel models of the Petri dish are used. The permittivity and the conductivity of the cells and those of the culture medium are obtained with Debye's dispersion equation. We measured the power pattern of the irradiator using the plane wave expansion (PWE) method, and developed a program module to calculate the FDTD-compatible incident field from the irradiator, whose position and orientation are adjustable. The MMW multiple reflection between the Petri dish and the irradiator is evaluated before being neglected. For the single-dish, double-dish and quadruple-dish exposure set-ups, the SAR intensity and the SAR uniformity are analysed and compared. The meniscus effect on the SAR distribution over the cell layer is evaluated for the single-dish set-up. The influence of the Petri dish interaction on the SAR distribution is examined for the double-dish and quadruple-dish set-ups.