Burgers' equation can be considered a special case of the one-dimensional Richards' equation for vertical flow for which the soil water diffusivity is constant and the unsaturated hydraulic conductivity is proportional to the square of the reduced water content. Here, a Fourier series solution for Burgers' (1948) equation for a finite region is presented. The solution is useful to modelers seeking a simplified representation of vertical water flow through the vadose zone and as an analytical solution for benchmarking which maintains many of the nonlinear characteristics of solutions to Richards' equation. Two example problems are presented. In the first, infiltration into a dry soil is modeled showing that Burgers' equation gives developing wetting front profiles similar to those observed for Richards' equation. In the second example, one-step outflow from an 8-cm core is modeled. Comparisons between the analytical and finite difference solutions for Burgers' equation are presented to help verify the analytical solutions. ¿ American Geophysical Union 1993