Soil temperatures are typically measured at shallow depths near the soil surface where large diurnal variations occur. For depths deeper than about 50 cm analytical and numerical models are often used to simulate the annual variations in daily temperature, which require information about the soil thermal diffusivity (D). An analytic solution to the onedimensional Fourier heat conduction equation was used by Matthias and Warrick (1987) to simulate daily soil temperatures at 20 and 100 cm depths at Safford, Arizona, and at 20 cm depth at Yuma, Arizona, using observed daily soil temperatures at 10 cm depth at each location and an estimate of the average soil thermal diffusivity as inputs. The solution was the sum of a deterministic (mean annual wave) component and a stochastic (daily fluctuations about the mean wave) component. The purpose of the research described in this paper is to use the model described by Matthias and Warrick (1987) to calculate the average thermal diffusivity for a semi-arid rangeland soil at the Page Ranch near Oracle, Arizona. The data used in this analysis were the daily soil temperatures at 50, 100, 300, and 500 cm depths observed during a one-year period from July 1, 1983 to June 30,1984 at the site. To obtain the average D, the daily temperatures at 50 cm depth and an initial estimate of D were input to the model to simulate temperatures at the 100, 300, and 500 cm depths. Observed and simulated temperatures at each depth were then compared. If the root-mean-square-deviations (RMSD) between observed and simulated values were large then an updated value of D was input to the model and temperature values recalculated. This trial-and-error approach continued until RMSD values were minimized. With D∼500 cm² d^-1 good agreement between observed and simulated temperatures was achieved with RMSD values ranging from 0.38 to 1.35 °C for the three depths.