There is a role for computer models in increasing the understanding of milk extraction from the human teat. A computer model can be used to investigate aspects of extracting milk from the human teat which are not feasible using clinical experiments. In this paper, the behavior of the human teat during an infant suckling and with the use of a breast pump is modeled. The model is used to (1) identify the role of suction and the peristaltic motion of the tongue during suckling and (2) compare the volume of milk extracted by an infant breastfeeding with that obtained using a breast pump. Infants use a peristaltic motion of the tongue, along with some suction, to extract milk. Breast pumps use a cyclic pattern of suction only. In the model, the human teat is represented as a cylindrical porous elastic material saturated with fluid. We mimic an infant suckling by imposing both suction and a peristaltic force in the computer model of the human teat. This is compared to the effect of suction only, which models the action of breast pumps. The results demonstrate that there is an optimal time to apply the peristaltic force during the suction cycle which will increase the milk volume. The model and results may be of use in the future design of effective breast pumps.