The authors derive a highly vectorising Green function recursion algorithm and a finite-size scaling description for diffusion in two-dimensional disordered systems. Extensive numerical calculations are presented for two different types of distribution function for the transfer rates between nearest-neighbour sites. The data are in good agreement with the dimensional crossover and scaling behaviour analytically predicted. Additionally, in contrast with one-dimensional systems with a box-shaped distribution of transition rates, they find no evidence for quasi-localisation. © 1988 American Institute of Physics.