This paper describes the numerical methods developed to simulate the transport of radionuclides through the unsaturated, fractured rock below the proposed repository at the Yucca Mountain. Regardless of the disposition of the Yucca Mountain License Application, this method has general applicability for modeling contaminant transport through deep vadose zones. Using a dual-permeability solution for fluid flow as a basis, the transport model represents contaminant transport with a cell-based particle-tracking technique in which particles move from cell to cell in the three-dimensional large-scale grid of two overlapping continua. Particle movement between cells, and the residence time within a cell, is computed probabilistically based on transfer functions using numerical solutions of the transport equations for an idealized fracture-matrix system. Using this approach, the following transport phenomena are simulated: advection through fracture and matrix continua, including between these continua, dispersion, sorption of dissolved radionuclides to the matrix continuum, and within the fault zones, and molecular diffusion between the fractures and matrix. In addition to providing a realistic representation of the relevant processes, this method has the virtue of computational efficiency. After describing the numerical method, this paper presents sensitivity analyses for radionuclide transport travel time distributions from the proposed repository to the water table through the unsaturated zone for the Yucca Mountain system.