We describe a method for the numerical computation of the propagation of primary and secondary nucleons, primary electrons, and secondary positrons and electrons. Fragmentation and energy losses are computed using realistic distributions for the interstellar gas and radiation fields, and diffusive reacceleration is also incorporated. The models are adjusted to agree with the observed cosmic-ray B/C and ¹⁰Be/⁹Be ratios. Models with diffusion and convection do not account well for the observed energy dependence of B/C, while models with reacceleration reproduce this easily. The height of the halo propagation region is determined using recent ¹⁰Be/⁹Be measurements as >4 kpc for diffusion/convection models and 4-12 kpc for reacceleration models. For convection models, we set an upper limit on the velocity gradient of dV/dz < 7 km s^-1 kpc^-1. The radial distribution of cosmic-ray sources required is broader than current estimates of the supernova remnant (SNR) distribution for all halo sizes. Full details of the numerical method used to solve the cosmic-ray propagation equation are given.