An approach is presented for approximating the expected spread rate of fires that burn across 2-dimensional landscapes with random fuel patterns. The method calculates a harmonic mean spread rate across a small 2-dimensional grid that allows the fire to move forward and laterally. Within this sample grid, all possible spatial fuel arrangements are enumerated and the spread rate of an elliptical fire moving through the cells is found by searching for the minimum travel time. More columns in the sample grid are required for accurately calculating expected spread rates where very slow-burning fuels are present, because the fire must be allowed to move farther laterally around slow patches. This calculation can be used to estimate fire spread rates across spatial fuel mixtures provided that the fire shape was determined from wind and slope. Results suggest that fire spread rates on random landscapes should increase with fire size and that random locations of fuel treatments would be inefficient in changing overall fire growth rates.