A geometric‐based simulation methodology was developed and incorporated into a computer code to model the hierarchical stratal architecture, and the corresponding spatial distribution of permeability, in braided channel belt deposits. The code creates digital models of these deposits as a three‐dimensional cubic lattice, which can be used directly in numerical aquifer or reservoir models for fluid flow. The digital models have stratal units defined from the kilometer scale to the centimeter scale. These synthetic deposits are intended to be used as high‐resolution base cases in various areas of computational research on multiscale flow and transport processes, including the testing of upscaling theories. The input parameters are primarily univariate statistics. These include the mean and variance for characteristic lengths of sedimentary unit types at each hierarchical level, and the mean and variance of log‐permeability for unit types defined at only the lowest level (smallest scale) of the hierarchy. The code has been written for both serial and parallel execution. The methodology is described in part 1 of this paper. In part 2 (Guin et al., 2010), models generated by the code are presented and evaluated.