The infiltration equation with a time-dependent surface flux is solved numerically for nonlinear conductivities, using first-integral and shooting techniques. The diffusivity and conductivity are both taken as power laws. The relative accuracy of the numerical technique is obtained by comparison with the case of linear conductivity, where an exact analytical solution exists. An approximate analytical result is given and compared with the solution for nonlinear conductivities from the shooting technique. It is found that the approximate analytical result is an excellent approximation to the exact numerical solution. It is also suggested that the solution obtained here can be used to validate the numerical solution of Richard's equation for arbitrary soil properties and arbitrary boundary conditions.