After examining the techniques used for solving the equations describing the propagation of cosmic-ray nuclei in the Galaxy, we have introduced a technique that yields exact numerical solutions for the steady state equations. We have implemented this in a new code, which uses the Runge-Kutta numerical method and incorporates current knowledge of relevant physical parameters to carry out simultaneous integration of the steady state equations. Comparing results from the steady state solution with those obtained using the weighted-slab approximation, we find that the weighted slab underestimates the equilibrium flux at low energies for all nuclei and does so most severely for secondary nuclei. At high energies, the fluxes of secondary nuclei also differ from the steady state results, depending upon the value of the parameter U, the ratio of the of the daughter and parent nuclei (A/Z). Rasy, the high-energy asymptotic ratio of the secondary fluxes obtained from the weighted-slab and steady state solutions, is well parameterized by the useful relationship Rasy = U-0.53. Our results are in qualitative, but not quantitative, agreement with the seminal work of Ptuskin, Jones & Ormes. We have determined the path length traversed by cosmic rays by making use of the steady state technique and the observed B/C ratio for various compositions of interstellar gas. Our results agree well with those derived by Webber, but vary from those of Heinbach & Simon.