A population of channels penetrates a soil matrix that is otherwise homogeneous. The channels are assumed to be vertical and of circular cross section with constant diameter, but channel depths and radii are allowed to vary over the population. This paper uses a model based on the Green‐Ampt assumptions to predict infiltration rates through the walls and bases of channels, resulting in a mathematical description of the way in which infiltration develops in the soil and in which channels fill with water until eventually overland flow is initiated. This model takes account of the fact that there may be a random distribution of channels in space. Expressions for the expected mean and variance of infiltration volumes are derived. Some example results are given and show that below the matrix wetting front the variance of the change in water content with 30 and 50 channels per square meter may be of the same order as the mean change in water content. The presence of channels can lead to significant increases in predicted channel volumes.