The diffusion coefficient associated with random walk of magnetic field lines is computed by direct calculation of a large number of field lines from a specified statistical ensemble. Two-component magnetic field models are examined, consisting of a mixture of slab and two-dimensional fluctuations. The scaling of the diffusion coefficient with magnetic field strength is established numerically for a wide range of relative fluctuation amplitudes (Δb/B0). The results confirm the recent nonperturbative theory of field line random walk (Phys. Rev. Lett., 75, 2136, 1995), but depart considerably from the quasilinear B-20 scaling, for models thought to be appropriate to the solar wind. ¿ American Geophysical Union 1996