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A deterministic method is described for performing three-dimensional (3D) photon transport calculations of a LINAC head and phantom/patient geometry to obtain dose distributions for therapy planning. The space, energy, and directional-dependent photon flux density is obtained by numerically solving the Boltzmann equation in general 3D geometry using the method of characteristics. The deterministic transport calculations use similar ray tracing routines as found in Monte Carlo (MC) codes. A special treatment is developed to better represent the impact of scattering from accelerator head components. Equations are presented for computing the water kerma distribution due to the uncollided and collided photon flux density field in the patient region. Kerma results obtained from the deterministic computation are compared to Monte Carlo values for a variety of source spectra and field sizes. The agreement for kerma values in the beam is usually within the MC uncertainties. It is concluded that the deterministic method is a rigorous, first-principles approach that could provide a superior alternative to Monte Carlo calculations for some types of problems. However additional development is needed to provide capability for 3D electron transport calculations.