A model is presented for predicting hourly soil temperatures under bare and residue plus plantcovered east-west oriented ridges in the Northern U.S. Corn Belt. The model is based on the implicit finite difference solution of a one-dimensional heat-flow equation. Two-dimensional soil temperature distribution under a ridge-furrow system is simulated by solving the one-dimensional heat-flow equation in vertical and horizontal directions, alternatively. Inputs needed for simulation are thermal diffusivity, and initial and boundary conditions. A procedure is suggested for estimating hourly upper boundary temperatures from daily maximum and minimum air temperatures. A constant temperature at the bottom boundary was justified by simulating soil temperatures in a deep profile. In general, the predicted soil temperatures under the bare ridge-furrow surface were within 2°C of the measured values; however, at some depths differences were as great as 4°C. Considering that soil temperatures are generally inputs to models (crop emergence and plant growth, nitrogen transformations and chemical degradation) that use at the minimum a daily time step, errors of 2-4°C in daily soil temperatures, in many cases, will lead to relatively minor errors in the final prediction of higher order processes.